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Now, ∠2-(3a – b)° [From (i)] 3k + 2k = 90° ⇒ 5k = 90° Solution: Now, PQ || RT and RQ is a transversal. ∴ ∠1 + ∠z = 180° (Co-interior angles) ∴ b = 50° [Alternate interior angles]. Solution: Solution: 60° + y = 90° b: If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is 180°. Measures (in degrees) of two supplementary angles are consecutive odd integers. (a) 100° Then, ∠QOS measures Two right angles are complementary to each other. 45 to 48). (d) both a and b are false (iv) ∠POR and ∠QOS; ∠ROQ and ∠POS are two pairs of vertically opposite angles. Solution: ∴ x + 2x = 180° In the given figure, line l intersects two parallel lines PQ and RS. In the given figure, if l || m, find the values of a and b. ∴ ∠1 = ∠2 [Alternate interior angles] Solution: Solution: The greater the angle, the better chance the player has of scoring a goal. Find the measures of two complementary angles if one angle is five times the other angle. You can check whether an angle is a right angle by using a set square, like in the picture below. Solution: Two adjacent angles always form a linear pair. ∴ ∠2 + 75° = 180° [Co-interior angles] Let x = 3k and y – 2k ∴ a = 45° [Corresponding angles] (b) Since, x + 90° = x – 90° (d) ∠2 + ∠3 = 180° Since, PQ || RS and TR is a transversal. ∠2 = ∠3 [Alternate interior angles] ∴ These angles are complementary. Name; Solution: (i) each pair of vertically opposite angles, and From (i) and (ii), we have and x – y = 30° ——— (ii) [Given] False In the given figure, find out which pair of lines are parallel: Solution: Solution: (a) 60°, 120° Then, Complementary angles are angle pairs whose measures sum to one right angle (1 / 4 turn, 90°, or π / 2 radians). No, two acute angles cannot form a pair of supplementary angles. (ii) ∠APS = ∠EPQ = 130° [Vertically opposite angles] But the angles don’t have to be together. Now, 40° + 90° + 5a = 180° [Angles on a straight line BOE] (c) alternate interior angles ∴These angles are supplementary. Question 1. ∴ a = f [Corresponding angles] (b) PQ is a straight line. In a pair of complementary angles, each angle cannot be more than _________ A transversal intersects two or more than two lines at _________ points. Question 86. (a) 36° If the two complementary angles are adjacent then they will form a right angle. ∴ ∠c + ∠2 = 180° [Linear pair] (d) 60° Question 97. Solution: Solution: (c) 70°, 110° Solution: (ii) PQ || UT and PT is a transversal. 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) vertically opposite angles Yes, because the sum of two angles is 180, and if they are both 90 degrees, they add up to 180, making them supplementary, and of the same measure, making them congruent. (a) 29° ∴ x + 2y + 3y = 180° (iii) d and f ⇒ (x – 10)° +(4x – 25)° + (x + 5)° = 180° [Angles on a straight line] (d) 62° Solution: ⇒ y = 90° – 60° = 30° ⇒ 50° = a As one acute angle and one obtuse angle can make two supplementary angles. (ii) each linear pair. Same, Question 48. (c) Estimate atleast two situations such that the angles formed by different positions of two players are complement to each other. Question 8. ∴ x = 110° [Alternate interior angles] Solution: (a) 36° Distinct. ⇒ ∠CDE-120° ——- (ii) [Using (1)] ∴ ∠2 + 3 = 180° [Co-interior angles] Question 29. Solution: In the given figure, PA || BC || DT and AB || DC. Solution: ⇒ x = 150°, Question 10. Question 70. And that is because their measures add up to 90 degrees. These two angles (40° and 50°) are Complementary Angles, because they add up to 90°: Notice that together they make a right angle. (b) Now the players are lined up as shown in Fig. The value of bis According to question, The reflex ∠EFG = 360° – 79° = 281°, Question 107. True (a) ∠1 = ∠3 ⇒ 5a = 180° + 20° = 200° (iii) There is no pair of vertically opposite angles and no angles are in the form of linear pair. (b) 100° Now, CD is a straight line. Write the correct one. Solution: According to question, Solution: Find the angles x and y. (b) ∠2 + ∠5 =180° (a) 40° but ∠2 + ∠3 = 180°, Question 39. (b) 61° (∵ 45° + 45° = 90° and 60° + 30°= 90°). From (i) and (ii), we get The measure of an angle's supplement is 44 degrees less than the measure of the angle. (d) 80°,100 ∠1 and ∠2; ∠1 and ∠4; ∠2 and ∠3; ∠3 and ∠4; ∠5 and ∠6; ∠5 and ∠8; ∠6 and ∠7; ∠7 and ∠8 are linear pairs. ⇒ ∠ABC = 180° – 120° [Using (ii)] ∴ The angles between North and West and South and East are supplementary. As vertically opposite angles are always equal but do not form a linear pair. Let the angle be x. (d) 120° ∴ ∠4 = 75° [Alternate interior angles], Question 91. (c) complementary True, Question 65. Now, ∠PQR = ∠PQU + ∠UQR Solution: Easy measure angles, using interactive whiteboard angle simulator. Solution: It will produce the same result. Two angles making a linear pair are always adjacent angles. ⇒ 30° + 5y = 180° Hence, a = 65° and b = 70°. Solution: Solution: Let one angle be x and other be y. Can two acute angles form a pair of supplementary angles? One of the complementary angles is said to be the complement of the other. ∴ ∠ABC + ∠CDE = 180° [Co-interior angles] Solution: Supplementary angles and complementary angles are defined with respect to the addition of two angles. In the given figure, PO || RS. Then, which one of the following is not true? ⇒ 60° – ∠L ——— (i) $$\Rightarrow \quad a=\frac{180}{5}=36$$ It is just a complete one angle. (i) Let the angle between b and c is ∠1. In figure, OB is perpendicular to OA and ∠BOC = 49°. (a) ∠TOS and ∠SQR is a pair of complementary angles. Solution: Supplmentary angles are two angles whose measures add to 180°. ⇒ ∠2 = 180° -60° = 120° ∴ x + 66° = 180° [Co-interior angles] Solution: (b) Since, POQ is a straight line According to question, Question 26. (c) 30°, 50° In the given figure, PO || RS, TR || QU and ∠PTR = 42°. ⇒ ∠COA = 90° – 49° [∵ ∠BOC = 49° (given)] Also, m is a straight line. An angle is 45°. If two angles have a common vertex and their arms form opposite rays (see figure). (a) Botha and bare true One obtuse angle and one acute angle can make a pair of supplementary angles. Adding (i) and (ii), we get Also, TR || QU and RS is a transversal. (d) supplementary angles In the given figure, state which pair of lines are parallel. (c) four pairs of adjacent angles. Question 45. 2 See answers profantoniofonte profantoniofonte Answer: … ∴∠PAB = ∠ABC [Alternate interior angles] (ii) ∠PQT and ∠PQR; ∠ORU and ∠QRP; ∠RPS and ∠RPQ are adjacent angles. ∴ ∠1 + ∠5 = 180° [By(i)and(iii)] $$\Rightarrow x=\frac{300^{\circ}}{3}=100^{\circ}$$ We have, Online protractor or angle problems with acute, obtuse, reflex angles. ∴ Let a = 3x and b – 2x As if both adjacent angles are acute angles, then they do not form a linear pair. What is the measurement of the other angle? Yes, 2 right angles can form a supplementary angle. Take any right angle and draw in a ray that has its endpoint as the vertex of the right angle. 614 views Solution: D. a supplementary angle. Complementary Angles. $$\Rightarrow \quad b=\frac{120^{\circ}}{3}=40^{\circ}$$ ∴ EF || GH A pair of complementary angles is angl… Get the answers you need, now! ∴ (a + b) + 65° = 180° [Co-interior angles] 90°, Question 55. These two are complementary because 27° + 63° = 90°. (c) 150° Hence, ∠a = 30°, ∠b = 150°, ∠c = 150°. and 2x + 3 = 2 × 44° + 3 = 88° + 3 = 91° (a) Seven football players are practicing their kicks. ⇒ ∠2 = 70° ——— (ii) corresponding angles are on the _________ side of the transversal. Solution: Find ∠EFD. Solution: The angles between North and West and South and East are (a) supplementary (i) toon(iii)up​, explain various security standards for internet​. (d) Since, x – 10° + 190°- x = 180° A pair of complementary angles is angles . Now, 60° + ∠1 = 60° + 120° = 180° and these angles are interior angles on the same side of transversal l. ADC and BDC are . (a) interior angles on the same side of the transversal ∴ ∠POQ + ∠QOR = 180° [Linear pair] ⇒ 3x = 180° We know that the sum of the measures of the complementary angles is 90° 2x + 2x + 2 = 90° sum of interior angles on the same side of a transversal is _________ (a) 110° Solution: Solution: 2. They may or may not be adjacent angles. 23° _____ One angle of a pair of supplementary angles is given. In the given figure, lines PQ and ST intersect at O. ∴ ∠3=68° ——– (i) [Corresponding angles] The result will be a pair of adjacent complementary angles. (c) p is false and q is true We have, ∴ ∠ABC + ∠BCD = 180° [Co-interior angles] According to question, In the given figure, POR is a line. Solution: Question 103. In Parts (a) and (b) given below, it may help to trace the diagrams and draw and measure angles. 45° : Given, angle = 45° (c) 30° Now, a || d and c is a transversal. Now, SP || RQ and PR is a transversal. Then, the angles are (iii) ∠TSV and ∠USV; ∠SVT and ∠SVU are adjacent angles. ∴ ∠QOS = 5 ∠POR = 5 × 15° = 75°, Question 23. ∠AOF=∠COD [Vertically opposite angles] Solution: Two supplementary angles are always obtuse angles. ⇒ 3a – b + 2a + b = 180 ⇒ 5a = 180 Now, EF || GH and AB is a transversal. Solution: (a) Let the two angles be x and 2x. (b) Since, PQ || ST and SO is a transversal. ⇒ 5a + 130° = 180° ⇒ ∠1 = 70° [Using (ii)] Find the angles. In the given figure, PQ is a mirror, AB is the incident ray and BC is the reflected ray. ∴ ∠1 = ∠3 [Corresponding angles] According to question, Complementary angles are always in a pair. (b) 67° ∴ a = 132 [Corresponding angles] Help Amisha in finding the angles. In each of the following figures, write, if any, Hence, it is not possible for two right angles to complement each other. $$\Rightarrow \quad x=\frac{200^{\circ}}{2}=100^{\circ}$$ (c) If one of the angles is right, then other angle of a linear pair is also right. Solution: ∠6 = ∠7 [Alternate exterior angles] Therefore the two smaller ones must add to 90° and so are complementary by definition). (a) 5b + 2a = 180° [Linear pair] (c) 36° ∠ABD and ∠DBC; ∠ABE and ∠CBE are linear pairs. Solution: Question 19. Question 42. Solution: Students can solve NCERT Class 7 Maths Lines and Angles MCQs Pdf with Answers to know their preparation […] True, Question 63. (c) 20° (d) Since, sum of the angles about a point is 360° Question 9. ∠1 = 120° [Vertically opposite angles] Solution: Solution: Solution: In the given figure, ∠AOC and ∠BOC form a pair of l || m and QR is a transversal. (iv) Let the angle between c and fig ∠4. 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Question 57. Solution: Vertically opposite angles are either both acute angles or both obtuse angles. Thus, ∠ABC = 60° and ∠CDE = 120°, Question 100. (c) ∠1 and ∠3; ∠2 and ∠4 are the two pairs of vertically opposite angles. Add your answer and earn points. ⇒ (6x – 30) = 180 ⇒ 6x – 180 + 30 = 210 (b) 90°, 90° ∴ Other angle is 180° – x. ⇒ 120° + ∠z= 180° [Using (i)] Two right angles are always supplementary to each other. If ∠ABC = 46°, then ∠ABP is equal to (c) ∠6 = ∠7 We have, 1 answer. ⇒ ∠2 = 180° – 135° = 45° C. an acute angle. Let each angle be x. ⇒ 50° + ∠QPR – 130° ⇒ 42° + ∠QUR = 180° [Using (i)] (b) In a pair of adjacent angles, vertex is always common, one arm is always common and their non-common arms are on either side of the common arm. when the owners were awa True (c) ∠3 + ∠8 = 180° ⇒ x = 90° – 79° ⇒ x – 11° Given that ∠AOB = 90° [∵ OB ⊥ OA] Question 85. (ii) one arm is always common, and Must add to 180° ( or a straight line MCQs for Class 7.... 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About complementary angles are equal lines at _________ points = 50 o, ∠ROQ = 40 o complementary. Than 90° of angle ABC is equal to 90° ( 30°+60° ) the ratio 1 5! Measure angles other angle of a pair of adjacent angles these 2 angles are supplementary to each other a!