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⇒ ∠c + 30° = 180° [Using (iii)] (c) 145° Solution: Solution: Question 60. They are lined up in a straight line in front of the goalpost [See fig.(i)). 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Now, a + b = 45° + 55° = 100°, Question 105. Solution: (c) ∠PQT and ∠TQS; ∠TQS and SQR; ∠PQT and ∠TOR; ∠PQS and ∠SQR are four pairs of adjacent angles. Solution: In the given figure, QP || RS. ∴ Its complement = 90° – x Now, QP || RS and PR is a transversal. ⇒ ∠BOC + ∠COA = 90° 60° + y = 90° (if a is perpendicular to b and b is perpendicular to c, then a is perpendicular to c) ... the measure of an … (b) 90°, 90° If an angle is 60° less than two times of its supplement, then the greater angle is ∠1 = ∠2 ——– (iii) [Verticallyopposite angles] (i) Since, PQ || UT and PT is a transversal. (c) complementary And we know that vertically opposite angles are equal. (a) (2 + b)° Solution: (b) ∠2 = ∠4 Solution: (c) 70°, 110° (a) ∠1 = ∠5 ... State whether the given statements are true or false: Question 1. (b) 45° False Draw two crossing lines. ∴ 90°- x = 79° In the given figure, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. In which of the following figures, a and bare forming a pair of adjacent angles? Solution: It is a right angle and measures 90°, Question 2: Look at the figure below and find ∠ACD, ∠ACB is a right angle According to question, Now, 40° + 90° + 5a = 180° [Angles on a straight line BOE] The diagram below shows a protractor. If two lines intersect at a point, then the vertically opposite angles are always _____ . ⇒ ∠POR + ∠QOS = 180° – 90° = 90° ——- (i) ∴ Its supplement = 180° – x (d) 150° ⇒ x + x = 180° [∵Angles are supplementary] \(\Rightarrow c=\frac{120^{\circ}}{4}=30^{\circ}\) ———– (i) The angles between North and West and South and East are As interior angles on the same side of a transversal with two distinct parallel lines are supplementary angles. For this example, I suggest a horizontal line. An angle may also be imagined as the figure formed by rotating a single ray about its vertex. ⇒ f = 108°, Question 37. Angles may be classified based on their angle magnitude. Vertically Opposite Angles. ∠AOF=∠COD [Vertically opposite angles] ∠APS + ∠PSC = 130° + 50° = 180° ⇒ 5a – 20° = 180° Filed Under: Geometry Tagged With: acute angle, Adjacent Angle, angle, complementary angle, Complete Angle, Exterior Angle, Interior Angle, obtuse angle, Reflex Angle, right angle, Straight Angle, supplementary angle, Vertically opposite angle, […] Complement angles add up to 90°. True (v) Sum of all interior angles of a quadrilateral is 180°. (d) both p and q are false 90°, Question 55. As two acute angles can make a pair of complementary angles. Answer. Putting value of x in (i), we get (ii) each linear pair. (c) 16° Sources. Find ∠PQR. f = c false . Angles which are both supplementary and vertically opposite are a : If two lines intersect, then the vertically opposite angles are equal. \(\Rightarrow \angle P O R=\frac{90^{\circ}}{6}=15^{\circ}\) In the given figure, PO || RS. (c) 64° Now, l || m and AC is a transversal. ⇒ ∠Q = 180° – 60° = 120°, Question 13. ∴ (a + b) + 65° = 180° [Co-interior angles] In the given figure, if l || m, find the values of a and b. Solution: 5.if a transversal intersects two lines and the corresponding angles are equal,then the two lines are parallel. In a pair of adjacent angles, The two angles are supplementary angles. ⇒ 60° + 20 = 180° c || f and a is transversal. (iii) uncommon arms are always opposite rays. As can be seen from the figure above, when two lines intersect, four angles are formed.Each opposite pair are called vertical angles and are always congruent.The red angles ∠ JQM and ∠ LQK are equal, as are the blue angles ∠ JQL and ∠ MQK. (c) alternate interior angles If two angles have a common vertex and their arms form opposite rays (see figure). Question 71. Vertically opposite angles are always (Vertical angles such as ... Then one of the alternate angles is an exterior angle equal to the other angle which is an opposite interior angle in the triangle. Sum of the measure of an angle and its vertically opposite angle is always. ∴ a = f [Corresponding angles] ⇒ ∠BCD = 180°- 50° = 130° = 35° + 55° [Using (6) & (ii)] Correct, there are 180° in the angle formed by any straight line. ∴ b = 48° ——— (i) Let one angle be 2x + 1, then the other angle is 2x + 3. Outer scale is marked in degrees from 0 to 180 from left to right. (a) 60°, 120° (d) (ii) is false (b) complementary angles (b) 50°, 20° (ii) EF is a straight line. (c) When a transversal cuts two parallel lines, each pair of interior angles on the same side of the transversal are supplementary. (a) how many angles are formed? If the sum of measures of two angles is 90%, then the angles are _________ ⇒ 720° = 5x (b) Since, PA || BC and AB is a transversal. 4.if a transversal intersect two lines, alternate angles are equal. . ∴ ∠COF = ∠EOD = 110° [Using (i)] [Vertically opposite angles] Now, 60° + ∠1 = 60° + 120° = 180° and these angles are interior angles on the same side of transversal l. In the given figure, examine whether the following pairs of lines are parallel or not: ⇒ x = 720° – 4x (i) vertex is always common, The side of a triangle that is opposite an angle greater than or equal to 180 is always the largest side of the triangle. Given two parallel lines are cut by a transversal, their same side exterior angles are congruent. (a) Since, POQ is a straight line. ∴ ∠POR + ∠ROT + ∠TOQ = 180° Interior angles on the same side of a transversal with two distinct parallel lines are complementary angles. ⇒ 2x + x = 180° ⇒ 5a + 130° = 180° (vi) Each interior angle of a n-sided regular polygon is \(\frac{(2 n-4) \times 90^{\circ}}{n}\). Thus, 30 degree and 60 degree are written as 30° and 60° respectively. ∴ Its supplement = 180° – x Measures (in degrees) of two complementary angles are two consecutive even integers. Solution: Answer: True. (c) ∠a + ∠d = 180° Write the correct one. (ii) ∠x and ∠y are complementary angles. Write down each pair of adjacent angles shown in the following figures: (d) A transversal cuts two … (i) ∠PSC = ∠RSF = 50° [Vertically opposite angles] Find the angles x and y. a = ∠1 + ∠2 = 60° + 30° = 90°. Solution: Solution: Acute, Question 54. The two vertically opposite angles are always equal. According to question, A straight angle is an internal angle which is equal to 180°. An angle which is half of its supplement is of ∴ In the given figure, two parallel lines l and m are cut by two transversals p and 4. Same, Question 48. So, this player has the best kicking angle. (a) supplementary (b) equal (c) unequal (d) none of these. We know that the sum of the measures of the complementary angles is 90° = 60° (d) 45°, 35° Solution: (i) False (ii) True (iii) True (iv) False (v) True (vi) True (vii) True 12. If one complete rotation is divided into 360 equal parts, the measure of each such part is one degree or 1°. ... 6.If the two lines being crossed are parallel lines,then the corresponding angles are equal. In the given figure, if AB || CD, ∠APQ = 50° and ∠PRD = 130, then ∠QPR is ∠EPQ+ ∠GQP = 130° + 50° = 180° (c) (i) is false but (ii) and (iii) are true ∴These angles are supplementary. ⇒ ∠2 = 180° – 135° = 45° Which of the following statements is false? Find ∠QUR. In the given figure, l, m and n are parallel lines, and the lines p and q are also parallel. Solution: (c) 79° Solution: Solution: For example, the player has a better chance of scoring a goal from Position A than from Position B. Thus, one angle is 45° and other is 180° – 45° = 135°, Question 98. ⇒ x = 180° – 66° = 114° An Interior Angle is an angle inside the shape ABC. According to question, Solution: Comment document.getElementById("comment").setAttribute( "id", "a45dd83c58a54e8143debfefdf41bd5a" );document.getElementById("da6c1f75c6").setAttribute( "id", "comment" ); © MathsTips.com 2013 - 2021. (b) 144° Question 81. (d) Since PQ I RS and line 1 is a transversal. Q. ∴ ∠RST + a = 180° [Linear pair] In the given figure, AE || GF || BD, AB||CG|| DF and ∠CHE = 120°. Solution: The angle which makes a linear pair with an angle of 61° is of b: If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is 180°. True False: Q 3: Any two adjacent angles have a common vertex. ... Property: If two lines intersect each other, then the vertically opposite angles are equal. (c) 100°, 60° Since, a transversal intersects two parallel lines, then interior angles on the same side of a transversal are supplementary. (vii) The diagonals of a trapezium, divide each other into proportional segments. \(\Rightarrow \quad x=\frac{88^{\circ}}{4}=22^{\circ}\) Let one angle be x. Solution: The supplement of the right angle is always _________ angle. Look at the figure above. True False: Q 2: Any two right angles are supplementary. ∠1 and ∠8; ∠2 and ∠7; ∠3 and ∠4; ∠4 and ∠5; ∠5 and ∠6; ∠3 and ∠6 are six pairs of supplementary angles. ∠ACD +30° = 90° Solution: True or False type of geometry questions 1. Question 103. ⇒ b = 180° – 132° = 48° Question 84. Find the measure of the segment. (d) ∠a = ∠d (b) 4th player has the greatest kicking angle. Line BC has been extended as line CD. They could be complementary in a highly skewed parallelogram in which one angle is 45 degrees. Now, c || d and e is a transversal. Vertically opposite angles are equal to each other. (b) 108° ⇒ ∠y = 180° – 35° = 145° ⇒ 3x = 180° It is denoted by ∠θ. From (i) and (ii), we have Maths Help, Free Tutorials And Useful Mathematics Resources. The greater the angle, the better chance the player has of scoring a goal. a and b are on the opposite side of transversal l. ∠POR + 5 ∠POR = 90° (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. ∴ ∠4 = 75° [Alternate interior angles], Question 91. Solution: Solution: Two angles that share the same vertex and one side are called adjacent angle. ⇒ ∠c = 180° – 30° = 150° ∠a = ∠3 [Vertically opposite angles] ∴ 6y + y + 2y = 180° 7.Angles in a same … Lines and Angles Class 7 MCQs Questions with Answers. (c) m and n are two straight lines and I is a transversal intersecting both lines m and n. 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