If two angles are complementary of each other, then each angle is: A. an obtuse angle. When two right angles are added, it is possible to get the supplementary angle. Now, e || f and c is a transversal. Solution: The result will be a pair of adjacent complementary angles. Solution: (d) 60° Since, PQ || RT and PR is a transversal. (d) 62° (d) 45°, 45° ⇒ ∠POR + ∠QOS = 180° – 90° = 90° ——- (i) ∠APS + ∠PSC = 130° + 50° = 180° Complementary angles are two angles that add up to 90°, or a right angle; two supplementary angles add up to 180°, or a straight angle. (i) Let the angle between b and c is ∠1. (a) Since, PQ || SR and RP is a transversal (ii) EF || GH ∴ x = 85° [Altemate interior angles] (b) Now the players are lined up as shown in Fig. $$\Rightarrow a=\frac{200^{\circ}}{5}=40^{\circ}$$, Question 14. In the given figure, line l intersects two parallel lines PQ and RS. What is the difference between supplementary angles and a linear pair? ∴ ∠1 + ∠x = 180° [Co-interior angles] Now, SOT is a straight line ⇒ 5a – 20° = 180° (a) 13 angles are formed. ⇒ 5b + 2 × 40° = 180° Solution: Determine the values of x and y. Then Given that $$\frac{x}{y}=\frac{3}{2}$$ In the given figure, lines and m intersect each other at a point. Solution: (a) 30° Since, 90° + 90° = 180°, a supplementary angle. ∴ ∠2 = ∠6= (34 – b)° ——– (i)[Corresponding angles] ∴ 2x + 1 = 2 × 44° + 1 = 88° + 1 = 890 Can two acute angles form a pair of supplementary angles? ∴ x + y = 85° + 50° = 135°, Question 41. ⇒ 6 ∠POR = 90° In the given figure, write all the pairs of supplementary angles. (c) (i) is false but (ii) and (iii) are true (c) one of its angles is right? and x – y = 30° ——— (ii) [Given] Add your answer and earn points. Solution: ⇒ 50° + ∠QPR – 130° Solution: but ∠4 ≠ ∠8, Question 38. Linear, Question 51. In a right angle triangle, as the measure of the right angle is fixed, the remaining two angles always form the complementary as the sum of … Let one angle be 2x + 1, then the other angle is 2x + 3. (a) 10° Since, QP || RS and QR is a transversal. Answer. Therefore the two smaller ones must add to 90° and so are complementary by definition). Since, vertically opposite angles are equal. (d) 80°,100 ⇒ ∠COA = 90° – 49° [∵ ∠BOC = 49° (given)] One angle of a pair of complementary angles is given. Solution: ⇒ 720° = 5x Question 18. (b) 11° ⇒ 3x = 180° (d) (ii) is false Hence, two right angles are never be complementary. (c) p is false and q is true (d) supplementary angles $$\Rightarrow x=\frac{166^{\circ}}{2}=83^{\circ}$$ In a pair of complementary angles, each angle cannot be more than _________ Kyuvaraj1034 is waiting for your help. This site is using cookies under cookie policy. An angle is 45°. Question 58. Now, ∠BOC = (x + 5)° = (35 + 5) = 40° As vertically opposite angles are always equal but do not form a linear pair. ∴ ∠PQR + ∠RQO = 180° [Linear pair] Give reason in support of your answer. ∴ (a + b) + 65° = 180° [Co-interior angles] ∠EPQ+ ∠GQP = 130° + 50° = 180° Supplementary angles: Two angles that add up to 180° (or a straight angle) are supplementary. (a) Since, POR is a straight line. Also, BC || DT and DC is a transversal. So, the sum of two right angles = 90° + 90° = 180°. Complementary angles: Two angles that add up to 90° (or a right angle) are complementary. Directions: If a transversal intersects two parallel lines, then answer (Q. ∴ ∠a = 30° [Using (ii)] $$\Rightarrow \angle A B P=\frac{134^{\circ}}{2}=67^{\circ}$$. Question 32. (b) supplementary Using the reflex angle, we can find the measure of the acute angle. (d) 45°, 35° = 264° + 132° = 396°. Solution: (b) 144° Now, PO is a straight line. (d) 80° So we can also say that angles DBA and angles ABC are complementary. These 2 angles (∠AOB and ∠AOC) are Complementary Angles, because they add up to 90° (30°+60°). Two lines AB and CD intersect at O (see figure). Solution: Answer: No. Thus, d = 142° So, this player has the best kicking angle. (d) ∠2 + ∠3 = 180° Solution: Thus, a = 67° and b = 48°, Question 102. $$\Rightarrow \quad x=\frac{176^{\circ}}{4}=44^{\circ}$$ (c) ∠1 and ∠3; ∠2 and ∠4 are the two pairs of vertically opposite angles. True ⇒ (3a + 5)° + (2a-25)° = 180° (c) 55° (c) alternate interior angles ⇒ (x – 10)° +(4x – 25)° + (x + 5)° = 180° [Angles on a straight line] One angle is complementary to the other or One angle is the complement of the other. Add your answer and earn points. (a) 90° (d) making a linear pair Solution: They can be adjacent angles but don’t have to be. In a pair of complementary angles, each angle cannot be more than_____. (iv) ∠POR and ∠QOS; ∠ROQ and ∠POS are two pairs of vertically opposite angles. Solution: (i) Yes, and b are the adjacent angles as they have a common vertex, one common arm and other non-common arms on the opposite side of the common arm. (c) adjacent Let the angle be x. Solution: (a) 20°, 50° Since sum of the these two angles are 90 o Measures (in degrees) of two complementary angles are two consecutive even integers. Find ∠AOD. Also, PQ || RS and line I is a transversal. (c) 16° (ii) ∠APS = ∠EPQ = 130° [Vertically opposite angles] Thus, ∠x = 60°, ∠y = 120°and ∠z = 60°, Question 92. ∠d = ∠c [Vertically opposite angles] Two right angles are complementary to each other. ⇒ x = 720° – 4x Solution: Directions: In questions 57 to 71, state whether the statements are True or False. Let each angle be x. (c) 80° ⇒ 5 ∠POR = ∠QOS ——– (ii) (a) ∠a = b In the given figure, AE || GF || BD, AB||CG|| DF and ∠CHE = 120°. No, two acute angles cannot form a pair of supplementary angles. (i)∠1 = 65° [Vertically opposite angles] An obtuse angle measures greater than 90° and less than 180°. (b) 15° Now, RS is a straight line. Question 89. ∴ y + 80° = 180° [Co-interior angles] If angle P and angle Q are supplementary and the measure of angle P is 60°, then the measure of angle Q is (d) 22.5° ∴ ∠1 = ∠3 = 30° ——— (ii) [Corresponding angles] Question 80. there was a theft in the temple and two houses were broke up. In the given figure, PO || RT. ⇒ ∠2 = ∠y = 120° [Vertically opposite angles] 1: m<1 is equal to 50 degrees. 1. ∴ ∠HCB =∠CDE [Corresponding angles] (a) Since, PQ || RS and RQ is a transversal Take any right angle and draw in a ray that has its endpoint as the vertex of the right angle. Can two acute angles form a pair of supplementary angles? a and b are on the opposite side of transversal l. What is the measurement of the other angle? l || n and q is a transversal. (d) ∠a = ∠d In the given figure, PO || SR and SP | RQ. Now, p || q and m is a transversal. (d) Let the angle be x. ⇒ 30° + 5y = 180° $$\Rightarrow c=\frac{120^{\circ}}{4}=30^{\circ}$$ ———– (i) In the given figure, lines PQ and ST intersect at O. Now, ∠PQR = ∠PQU + ∠UQR Vertically opposite angles are either both acute angles or both obtuse angles. Question 3: Can two right angles complement each other? (b) 67° A supplementary angle makes a straight line. ∠6 = ∠7 [Alternate exterior angles] Now, e || f and d is a transversal. Solution: Let one angle be x. Ex. (c) 90° Solution: (iii) There is no pair of vertically opposite angles and no angles are in the form of linear pair. (d) adjacent but not supplementary but ∠a ≠ ∠d, Question 12. Solution: ∴ b = 70° [Corresponding angles] Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees (right angle). (d) 20° p: a and bare forming a linear pair. Distinct. (c) Since, angles are on a straight line. 1 answer. ⇒ x + 2x = 300° Write down each pair of adjacent angles shown in the following figures: ∴ ∠1 = ∠2 [Alternate interior angles] Parallel, Question 50. (c) The angle between South and West is a right angle and angle between South and East is also a right angle. Find each of the angles. Question 24. ⇒ ∠x + ∠2 = 180° [Co-interior angles] When talking about complementary angles, it's important to remember that they're always in apair. (b) ∠2 + ∠5 =180° (b) 30° Find the measures of two complementary angles if one angle is five times the other angle. Solution: Solution: ∴ ∠2 + ∠5 = 180° —— (i) [Co-interior angles] A + B = 90° (c) 36° Solution: Question 42. ∴ AB || CD (ii) AB and CD But the angles don't have to be together. Interior angles on the same side of a transversal with two distinct parallel lines are complementary angles. Also, m || n and p is transversal. (a) Let the angles be x and y. Thus, one angle is 100° and other is 80°. (d) ∠4 = ∠8 Its complementary angle must be less than 45°. In each of the following figures, write, if any, (c) (108 – b)° The difference of two complementary angles is 30°. $$\Rightarrow \quad k=\frac{90^{\circ}}{5}=18^{\circ}$$ From (i), Solution: In the given figure, POR is a line. Solution: Thus, the required angles are 60° and 30°. ∴ ∠POR + ∠ROS + ∠QOS = 180° ⇒ ∠2 = (3 × 36 – b)° = (108 – b)°, Question 36. Question 75. ∴ A and bare alternate interior angles. ⇒ ∠AOD = 180°- 41° [Using (1)] Find the angles. The measure of an angle's supplement is 44 degrees less than the measure of the angle. ⇒ x + 210° = 360° What is the type of other angle of a linear pair if ∴ AOB is a straight line. (i) toon(iii)up​, explain various security standards for internet​. (b) ∠d=∠c Let one angle be x and other be y. True, Question 69. (a) (2 + b)° ∴ ∠POQ + ∠QOR = 180° [Linear pair] So, this player has the best kicking angle. ⇒ 3x = 180° Hence, a = 65° and b = 70°. $$x=\frac{180^{\circ}-x}{2}$$ (c) 13° Now, l || m and n is a transversal. Solution: Then, (c) 70°, 110° ∴ ∠2 + 75° = 180° [Co-interior angles] The value of a is Online protractor or angle problems with acute, obtuse, reflex angles. (b) 144° A transversal intersects two or more than two lines at _________ points. but ∠2 + ∠3 = 180°, Question 39. ⇒ ∠QPR = 130° – 50° = 80°, Question 11. From (i) and (ii), we have ⇒ ∠1 = 70° [Using (ii)] False. (b) ∠4 = ∠8 ⇒ 9y = 180° In the given figure, POQ is a line. ⇒ 5b – 180° – 80° = 100° (c) ∠PQT and ∠TQS; ∠TQS and SQR; ∠PQT and ∠TOR; ∠PQS and ∠SQR are four pairs of adjacent angles. ∴ 4c = 3b    [Corresponding angles] Also, LM || SR and TS is a transversal. and its supplement = 180° – x= 180°- 100 = 80° ∠FOR + ∠QRH = 123° + 57° = 180° ∴ ∠1 + ∠5 = 180° [By(i)and(iii)] (d) 30° Now, PQ || RT and RQ is a transversal. (b) We know that angle of incident and angle of reflection is same. (d) Since, sum of the angles about a point is 360° Use the diagram to identify the special angle pairs. (b) p is true and q is false ∴ x + 64° + 46° +100° – 360° ∴ x + y = 180° ———– (i) As a linear pair has one acute angle and one obtuse angle. (c) both are acute Question 96. In the given figure, the value of a is Solution: (a) If one of the angles is acute, then other angle of a linear pair is obtuse. In the given figure, PO || RS, TR || QU and ∠PTR = 42°. ⇒ y = 180° – 48° = 132° 2x = 180° + 20° = 200° ∠1 +∠2 = 180° [Angles on a straight line PQ] ∴ a = 3x = 3 × 36° = 108° We know that when the measure of an angle is exactly 90°, then it is known as a right angle. Now, l || m and p is a transversal. Question 30. Solution: If an angle is 60° less than two times of its supplement, then the greater angle is x + x = 166° This construction takes a given angle and constructs its complementary angle. $$\Rightarrow \quad x=\frac{200^{\circ}}{2}=100^{\circ}$$ In the given figure, PA || BC || DT and AB || DC. ∴ b = 50° [Alternate interior angles]. (d) 120° ⇒ ∠CDE-120° ——- (ii) [Using (1)] As two acute angles can make a pair of complementary angles. ∴These angles are supplementary. Since, a transversal intersects two parallel lines, then interior angles on the same side of a transversal are supplementary. ⇒ 90° – 62° = x $$\Rightarrow x=\frac{120^{\circ}}{2}=60^{\circ}$$ ⇒ ∠2 = 180° – 75° = 105° Solution: Question 97. If two supplementary angles are in the ratio 1 : 2, then the bigger angle is ∴ The bigger angle is 2x = 2 × 60° = 120°. ∴ Its complement = 90°- 45° = 45°, Question 56. Hence, it is not possible for two right angles to complement each other. ⇒ ∠3 – 180° – 105° = 75° [From (ii) part] Learn how to define angle relationships. (ii) ∠PQT and ∠PQR; ∠ORU and ∠QRP; ∠RPS and ∠RPQ are adjacent angles. (a) 95° (b) complementary (iii) uncommon arms are always opposite rays. (ii) EF is a straight line. Solution: No, two acute angles cannot form a pair of supplementary angles. Question 3. Statements a and bare as given below: (b) 4th player has the greatest kicking angle. ⇒ 60° + 20 = 180° We hope the NCERT Exemplar Class 7 Maths Chapter 5 Lines and Angles will help you. If two angles add up to 180o they are _____ angles. (d) both p and q are false (iv) No, a and b are not adjacent angles as the arms which are not common are on the same side of common arm. NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12. False = 90°. ⇒ b = c – a ∴ y + 48° = 180° [Co-interior angles] ∴ ∠ABC + ∠BCD = 180° [Co-interior angles] Then, ∴∠CHE = ∠HCB – 120° ———- (i) [Alternate interior angles] In a right triangle, the two smaller angles are always complementary.(Why? 2 See answers profantoniofonte profantoniofonte Answer: … (a) vertically opposite angles What is a Complementary Angle? ∴ ∠x = 35° [Alternate interior angles] ⇒ 130° = b Since, AF || ED and FD is a transversal. As interior angles on the same side of a transversal with two distinct parallel lines are supplementary angles. ∠1 and ∠2; ∠1 and ∠4; ∠2 and ∠3; ∠3 and ∠4 are four pairs of adjacent angles. Since, l || m and is a transversal. ADC and BDC are . Solution: ⇒ ∠2 = 180° – 135° = 45° (iii) Let the angle between d and fis ∠3. Opposite, Question 49. Two adjacent angles always form a linear pair. Solution : False Measure of right angle is 90°. According to question, 180°, Question 46. The C in complementary can be used to form the 9 in 90. ⇒ 3x = 180° – x ⇒ 3x + x = 180° Also, p || q and l is a transversal. ∠1 = 120° [Vertically opposite angles] (c) 5° Since, AB || l and EF is a transversal. An angle which is half of its supplement is of ∴ (b) 50° ⇒ 130° + y = 180° Find the values of a, b and c. ∴ ∠1 = 34° [Alternate interior angles] Then, which of the following is true? (c) Draw a line L.M passing through T such that LM || QP || SR. $$\Rightarrow x=\frac{720^{\circ}}{5}=144^{\circ}$$, Question 16. ∴ 6a = 120° [Corresponding angles] Now, PQ || RS and PR is a transversal. ∴ Its complement = 90° – x Question 74. The drawings below (see figure), show angles formed by the goalposts at different positions of a football player. Solution: ⇒ x + x = 180° [∵Angles are supplementary] (a) both p and q are true Question 90. Solution: (i) ∠PSC = ∠RSF = 50° [Vertically opposite angles] ∴ AB and CD are not parallel lines. ⇒ ∠c = 180° – 30° = 150° ⇒ ∠QUR = 180° – 42° = 138°. ⇒ ∠y = 180° – 35° = 145° Solution: ∴ 4c = 120°      [Corresponding angles] $$\Rightarrow \angle P O R=\frac{90^{\circ}}{6}=15^{\circ}$$ ⇒ ∠z = 180° – 120° = 60° Thus, a = 20°, b = 40° and c = 30°, Question 109. Now, CH || DF and CD is a transversal. Thus the required angles are 90° each. (a) ∠1 = ∠5 ∴ ∠QRS – ∠TSR = 85° ———- (ii) [Using (i)] [Alternate interior angles] Recall that the complementary angle is one that makes the given angle become 90°. (d) (180 – b)° Also, TR || QU and RS is a transversal. ∠2 = ∠4 [Corresponding angles] ∴ ∠c + ∠2 = 180° [Linear pair] because 90° + 90° = 180°, as it satisfies the condition of supplementary angles. Explanation: Angle equal to 90 o is called right angle. ⇒ 4x = 180° Find ∠EFD. ⇒ 5y = 180° – 30° = 150° Adding (i) and (ii), we get Solution: B. a right angle. Name; Find ∠QUR. Solution: (b) Since, PA || BC and AB is a transversal. (c) 45° (d) equal True, Question 64. Two supplementary angles always form a linear pair. We have, Arm, Question 47. (b) a is true and b is false The reflex ∠EFG = 360° – 79° = 281°, Question 107. In the given figure, a = 40°. Thus, the angle which is half of its supplement is of 60°. Question 112. (ii) Name all the pairs of complementary angles. Solution: Try These: Question 1: Which pairs of following angles are complementary? $$x=\frac{1}{3}\left(180^{\circ}-x\right)$$ ⇒ ∠2 = 180° -60° = 120° ⇒ x = 180° – 61° = 119° Same, Question 48. Question 5. ∴ ∠RSC + ∠CSF = 180° [Linear pair] $$\Rightarrow x=\frac{180^{\circ}}{5}=36^{\circ}$$ (c) If one of the angles is right, then other angle of a linear pair is also right. One obtuse angle and one acute angle can make a pair of complementary angles. ∴ ∠PQR – ∠QRS = 85° ———– (i) [Alternate interior angles] (b) 45° False ∠1 = ∠2 ——– (iii) [Verticallyopposite angles] ∴ ∠COF = ∠EOD = 110° [Using (i)] [Vertically opposite angles] (d) 144° Write the correct one. ∴ ∠5 = ∠8 [Alternate interior angles], Question 40. ⇒ x = 180° – 66° = 114° (iii) ∠1 and ∠2, ∠3 and ∠4, ∠5 and ∠6 are three pairs of supplementary angles. (b): Since, vertically opposite angles are equal. (a) supplementary Solution: If two angles have a common vertex and their arms form opposite rays (see figure). And just as another point of … Solution: The sum of two vertically opposite angles is 166°. (c) ∠3 + ∠8 = 180° As two right angles are supplementary to each other. Solution: ∴ ∠AOD = 139°, Question 94. Hence, ∠a = 30°, ∠b = 150°, ∠c = 150°. An angle is more than 45°. 45° : Given, angle = 45° How do you think about the answers? Then, ∠QOS measures Sum of two right angles is 180° which is double the sum of two complementary angles. In which of the following figures, a and bare forming a pair of adjacent angles? 60°: Let the angle be x. Now, l is a straight line. Solution: (b) Since, PQ || ST and SO is a transversal. ⇒ 85° + a = 180° [Using (ii)] ⇒ ∠b = 180° – 30° = 150° [Using (1)] If the sum of two angles is 180 degrees then they are said to be supplementary angles, which forms a linear angle together.Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together. If the two complementary angles are adjacent, their non-shared sides form a right angle. Solution: ∴ x = 110° [Alternate interior angles] a: If two lines intersect, then the vertically opposite angles are equal. ∴ a = 45° [Corresponding angles] Complementary Angles. Question 21. So the measure of angle DBA plus the measure of angle ABC is equal to 90 degrees. (c) 30° Supplmentary angles are two angles whose measures add to 180°. (c) 20°, 50° Question 25. Easy measure angles, using interactive whiteboard angle simulator. x + 61° = 180° [Linear pair] ∴ AB || CD. In the given figure, show that Since  ∠AOC and ∠BOC have a common vertex O, a common arm OC and also, their non-common arms, OA and OB, are opposite rays. ⇒ 120° + ∠z= 180° [Using (i)] In (given figures) are the following pairs of angles adjacent? Question 45. Solution: ⇒ 2x = 180° ⇒ x = 90° The legs of a stool make an angle of 35″ with the floor as shown in figure. ⇒ ∠2 = 180° – (2a+ b)° ——– (ii) [∵ ∠1 = (2a + b)° (given)] ∴ y = 2 × 18° = 36° 3k + 2k = 90° ⇒ 5k = 90° Solution: Therefore, B will be less than 45°. (d) supplementary Solution: ⇒ 100° + a = 180° (d) 119° If the sum of measures of two angles is 180° then they are _________ [ ∵∠AOE = 30° and ∠DOB =40° (given)] Question 77. If ∠1 = (2a + b)° and ∠6 (3a – b)°, then the measure of ∠2 in terms of b is (c) 100°, 60° A pair of complementary angles is angles . ∴ ∠COD = 90° Solution: (d) Vertically opposite angles are always equal. Complementary Angles. Given that ∠AOB = 90° [∵ OB ⊥ OA] (i) Since, PQ || UT and PT is a transversal. (a) 35° The measure of an angle which is four times its supplement is ⇒ x = 360° – 2x – 60° Amisha makes a star with the help of line segments a, b, d, e and f, in which a || d, b || e and c || f. Chhaya marks an angle as 120° as shown in figure, and asks Amisha to find the ∠x, ∠y and ∠z. Solution: ⇒ 5x = 180° (a) Since, ∠P + ∠Q = 180° (a) ∠1 + ∠5 = 180° ⇒ ∠COA – 41° ——— (i) Question 1. (d) 120° ∴ ∠LTS = ∠TSR [Alternate interior angles] In the given figure, if AB || CD, ∠APQ = 50° and ∠PRD = 130, then ∠QPR is Directions: In questions 42 to 56, fill in the blanks to make the statements true. Now, 60° + ∠1 = 60° + 120° = 180° and these angles are interior angles on the same side of transversal l. (c) 136° (a) 40° Thus, one angle is 89° and other is 91°, Question 99. ∴ Angles between South and West and South and East are making a linear pair. (d) 120° ⇒ ∠BOC + ∠COA = 90° (b) 125° (a) 100° ∠a = ∠3 [Vertically opposite angles] ⇒ (3a – b)° = 180° – (2a + b)° One obtuse angle and one acute angle can make a pair of complementary angles. Since, PQ || RS and TR is a transversal. (ii). ⇒ ∠EOD = 180° -30° – 40° = 110° ——— (i) (iii) No, a and b are not adjacent angles as they don’t have common vertex. Two supplementary angles are always obtuse angles. We have, (a) 4th player has the greatest kicking angle. Solution: (b) complementary angles. According to question, Solution: Solution: $$\Rightarrow \quad x=\frac{88^{\circ}}{4}=22^{\circ}$$ Question 35. ∠a + ∠d = 180° [Linear Pair] ⇒ 4 × 30° = 3b      [using (i)] Now, AB || DC and BC is a transversal. EASY. They just need to add up to 90 degrees. Now, l || m and AC is a transversal. (a) 5b + 2a = 180° [Linear pair] In Parts (a) and (b) given below, it may help to trace the diagrams and draw and measure angles. Example 2: 60°+30° = 90° complementary and adjacent Example 3: 50°+40° = 90° complementary and non-adjacent (the angles do not share a common side). Also, ∠EFG = ∠1 + ∠2 – 34° +45° = 79° (c) write all the pairs of vertically opposite angles. complimentary angles add up to 90 and a right angle is 90 degrees so the answer is always. Angles between South and West and South and East are Two right angles are always supplementary to each other. (i) ∠1 and ∠3; ∠2 and ∠4; ∠5 and ∠7; ∠6 and ∠8 are four pairs of vertically opposite angles. Question 67. So an angle of 30° has a supplementary angle of 90° - 30° = 60°. (a) 150° [∵ ∠P and ∠Q are supplementary angles] Thus, x = 114° and y = 132°, Question 108. In the given figure, the value of y is Question 82. Write all the pairs of adjacent angles by taking angles 1, 2, 3, and 4 only. Give reason. One of the complementary angles is said to be the complement of the other. In the given figure, if PQ || RS and QR || TS, then the value of a is $$\Rightarrow a=\frac{50^{\circ}}{5}=10^{\circ}$$, Question 27. ∴ ∠PQT = ∠LTQ [Alternate interior angles] True. 100° + y = 180 ⇒ y = 180° – 100° = 80° Solution: Solution: Acute, Right, Obtuse, Straight, Reflex & Complete angle. Now, a || d and c is a transversal. (iii) ∠TSV and ∠USV; ∠SVT and ∠SVU are adjacent angles. (d) 60° Example: From the above example ∠POR = 50 o, ∠ROQ = 40 o are complementary angles. In a pair of adjacent angles, ⇒ 3a – b = 180 – 2a – b Two Angles are Supplementary when they add up to 180 degrees. (d) 64° As if both adjacent angles are acute angles, then they do not form a linear pair. (b) Since, POQ is a straight line ⇒ z + 36° = 180° ⇒ z = 180° – 36° = 144°, Question 31. (d) ∠a = ∠b [Vertically opposite angles] Question 57. Complementary angles are two angles whose measures add to 90°. ∴ a = f [Corresponding angles] (b) 70°, 40° In the given figure, two parallel lines l and m are cut by two transversals n and p. Find the values of x and y. ⇒ 3x = 300° 2x + 2x + 2 = 90° Solution: Also, RQ || TS and RS is a transversal. Solution: Complementary angles are pair angles with the sum of 90 degrees. 0 0. $$\Rightarrow \quad a=\frac{180}{5}=36$$ ∴ Let each angle be x. Question 4. ∴ Its supplement = 180° – x (b) ∠2 = ∠4 Solution: ∴ EF and GH are not parallel lines. ⇒ 4x = 90° – 2 = 88° Question 20. ⇒ d = 180°- 38° = 142° [Using (i)] Solution: ∴ ∠ABP = ∠CBQ ——– (1) Solution: In this example, let's put some Algebra to work to find the measure of two angles whose sum equals 90 degrees, better knows as complementary angles. Solution: $$\Rightarrow \quad x=\frac{210}{6}=35$$ (iv) c and f Then, f is equal to ADC and BDC are . Solution: Thus, one angle is 45° and other is 180° – 45° = 135°, Question 98. (d) 10° Two lines in a plane which do not meet at a point anywhere are called _________ lines. Supplementary angles and complementary angles are defined with respect to the addition of two angles. corresponding angles are on the _________ side of the transversal. (a) 110° 4.Two angles that are right are always congruent. Given points A, O and B are collinear. 90° – x = 62° We have ⇒ 42° + ∠QUR = 180° [Using (i)] In figure, OB is perpendicular to OA and ∠BOC = 49°. Solution: (a) 130° Obtuse, Question 52. (c) 30°, 50° ∴ Other angle is 180° – x. Solution: $$\Rightarrow y=\frac{150^{\circ}}{5}=30^{\circ}$$ Solution: 90°, Question 55. Then, the angles are - one angle is 90° and all three add up to 180°. (a) interior angles on the same side of the transversal ∴ ∠APR = ∠PRD [Alternate interior angles] x = 4 (180° – x) Question 71. ⇒ y = 180° – 30° = 50° As one acute angle and one obtuse angle can make two supplementary angles. Question 33. Now, a + b = 180° [Angles on a straight line PQ] (c) ∠5 = ∠8 Solution: The two angles do not need to be together or adjacent. alternate interior angles have one common _________ Solution: (c) ∠6 = ∠7 (b) 60° Solution: They may or may not be adjacent angles. (a) 120° (i) Name all the pairs of adjacent angles. Solution: Use on interactive whiteboards, angles can be automatically shown or measured with a protractor. (i) ∠AOB and ∠BOC; ∠AOC and ∠COD; ∠AOB and ∠BOD; and ∠BOC and ∠COD are adjacent angles. (d) Since, PQ || RS, line l is a transversal. ⇒ x + 4x = 720° ∴ EF || GH Measures (in degrees) of two supplementary angles are consecutive odd integers. Thus, x = 110° and y = 100°. (a) 120° The supplement of the right angle is always _________ angle. Question 78. As ∠RSP and ∠QPD are corresponding angles and are not equal. ⇒ 5a = 180° + 20° = 200° Maths MCQs for Class 7 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. According to question, (b) how many types of angles are formed? ∠1 and ∠8; ∠2 and ∠7; ∠3 and ∠4; ∠4 and ∠5; ∠5 and ∠6; ∠3 and ∠6 are six pairs of supplementary angles. A pair of complementary angles is angl… Get the answers you need, now! One angle is the complement of the other angle. (d) both are obtuse We know that the sum of the measures of the supplementary angles is 180°. ∴ 6y + y + 2y = 180° In the given figure, 4m and a line t intersects these lines at P and Q, respectively. (c) Since, PQ || RS and line 1 is a transversal. (a) 95°, 85° (ii) No, a and b are not adjacent angles as they don’t have common arm. Solution: An acute angle measures greater than 0° and less than 90°. We have, There is an easy way to try and remember these using the first letters of each word. $$\frac{\angle P O R}{\angle Q O S}=\frac{1}{5}$$ Question 86. (b) 50°,130° Also, a || d and f is a transversal. Solution: The angles between North and West and South and East are ⇒ b = 180° – 132° = 48° (b) If one of the angles is obtuse, then other angle of a linear pair is acute. ⇒ ∠Q = 180° – 60° = 120°, Question 13. ⇒ a = 180° – 100° = 80°. (a) Both statements p and q are true. Solution: And that is because their measures add up to 90 degrees. You can think of them as two puzzle pieces that form one 90 degree angle when they are put together. Complementary, Question 43. The supplement of an acute is always _________ angle. ⇒∠APQ + ∠QPR = 130° ∴ ∠2 = 30° [Corresponding angles] (d) 101° Solution: In the given figure, P, Q and R are collinear points and TQ ⊥ PR, ∴ ∠AOD + ∠AOC = 180° [Linear pair] ∠1 = 120° ———- (i) [Vertically opposite angles] The reflex angle can be calculated if the measure of the acute angle is given, as it is complementary to the acute angle on the other side of the line. (iv) ∠AOC and ∠AOD; ∠BOC and ∠BOD; ∠AOC and ∠BOC, ∠AOD and ∠BOD are adjacent angles. Hence, ∠x = 35° and ∠y = 145°. (d) ∠3 = ∠7 ⇒ 90° + x + y = 180° Now, p || q and n is a transversal. (b) complementary angles (∵ 45° + 45° = 90° and 60° + 30°= 90°). ⇒ x+y – 90° ——- (i) If x= 30°, then ∠QOR is Question 87. ∴ ∠2 + 3 = 180° [Co-interior angles] (a) supplementary NCERT Exemplar Class 7 Maths Chapter 5 Lines and Angles are part of NCERT Exemplar Class 7 Maths. Solution: Then, the values of a and bare respectively. Angles which are both supplementary and vertically opposite are The Right angles can make a pair of complementary angles- _________, there have been several thefts in the houses in your locality. (i) ∠AOD and ∠DOB; ∠DOB and ∠BOC, ∠BOC and ∠AOC; ∠AOC and ∠AOD are four pairs of supplementary angles. ∴ x + y = 90° ———(i)     [Angles are complementary] Question 2. It is just a complete one angle. Let A and B are two angles making a complementary angle pair and A is greater than 45° ∴ ∠4 = 75° [Alternate interior angles], Question 91. (b) Since, x + 90° = x – 90° ∴ ∠RST + a = 180° [Linear pair] ∴ ∠TRU + ∠QUR = 180° [Co-interior angles] Here we have given NCERT Exemplar Class 7 Maths Solutions Chapter 5 Lines and Angles. (c) If one of the angles is right, then other angle of a linear pair is also right. (a) one of its angles is acute? Question 103. Its complement -90° – x (a) 44° Supplementary, Question 44. Since, angles are supplementary Solution: Solution: Supplementary Angles. ∴ Its supplement = 180° – x As ∠EPQ and ∠GQP are interior angles on the same side of transversal AB and are supplementary ⇒ ∠RQU = 35° ——- (ii) ∴ x + 66° = 180° [Co-interior angles] ∴ b + d = 180° [Co-interior angles] (c) alternate interior angles Now, EF || GH and AB is a transversal. Solution: In the given figure, QP || RS. z + y = 180° [Linear pair] (a) 36° ∠ABD and ∠DBC; ∠ABE and ∠CBE are linear pairs. Question 68. a = ∠1 + ∠2 = 60° + 30° = 90°. Solution: From (i) and (ii), we get (b) 24° ⇒ 50° = a The Right angles can make a pair of complementary angles- _____ 1 See answer Kyuvaraj1034 is waiting for your help. Also, AB || DF and BD is a transversal. The angle which makes a linear pair with an angle of 61° is of In the figure above, the two angles ∠ PQR and ∠ JKL are complementary because they always add to 90° Often the two angles are adjacent, in which case they form a right angle.. ∴ a = 36 (b) Let the angle be x. These two are complementary because 27° + 63° = 90°. ∴ ∠AOE + ∠EOD + ∠DOB = 180° ∴ The angles between North and West and South and East are supplementary. ∴ ∠TUR = ∠UVQ = 122° [Corresponding angles] These angles aren’t the most exciting things in geometry, but you have to be able to spot them in a diagram and know how to use the related theorems in proofs. ⇒ ∠RSC = 180° – 65° = 115° In the given figure, l, m and n are parallel lines, and the lines p and q are also parallel. Constructs its complementary angle is the difference between supplementary angles is right conditions of storing and cookies!, 9, 10, 11 and 12 ∠BOD are adjacent then can! ∠Aoe = 30° [ Corresponding angles ] Now, l || m and p a... Cd and FG is a transversal with a protractor then, the sum of measures of two complementary angles consecutive! Meet at a point find the measures of two right angles can make a pair of opposite! That two angles are adjacent, their non-shared sides form a linear pair is acute,,., respectively and ∠RPQ are adjacent angles and a: b = 50° [ Alternate interior angles ] Question... || DT and AB is a transversal intersects two or more than two lines at points! ∠Tor ; ∠SQR and ∠PQS are two pairs of adjacent angles angle involves! 100° = 80° degrees so the answer is always _________ angle Solutions Chapter 5 lines and ;. The statements true iv ) ∠AOC and ∠BOC, ∠AOD and ∠BOD are adjacent angles but don ’ have! 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