Solution: Question 8. Two vertically opposite angles are always equal. (b) p is true and q is false ∴ x + y = 180° ———– (i) ⇒ 50° + ∠QPR – 130° (iii) No, a and b are not adjacent angles as they don’t have common vertex. 2. true or false: planes are created by 3 collinear points. Solution: Write all the pairs of adjacent angles by taking angles 1, 2, 3, and 4 only. If they were supplementary, they would not be vertical angles. ∴ ∠x = 35° [Alternate interior angles] There are three types of angles formed by parallel lines and a transversal. If angle P and angle Q are supplementary and the measure of angle P is 60°, then the measure of angle Q is ∴ Its complement = 90°- 45° = 45°, Question 56. Solution: (d) ∠AOC and ∠BOC form a pair of supplementary angles. In the given figure, PQ, RS and UT are parallel lines. (d) ∠4 = ∠8 ∴ 2x = 2 × 22° = 44° and 2x + 2 = 44° +2 = 46° Always. Arm, Question 47. As ∠RSP and ∠QPD are corresponding angles and are not equal. As, PQ is a straight line. If you have any query regarding NCERT Exemplar Class 7 Maths Solutions Chapter 5 Lines and Angles, drop a comment below and we will get back to you at the earliest. Solution: In the given figure, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. Introduction to Point, Ray, Line and Line-Segment, Click to share on Facebook (Opens in new window), Click to share on Twitter (Opens in new window), Click to share on LinkedIn (Opens in new window), Click to share on Reddit (Opens in new window). (False) (vi) 30° is one-half of its complement. (a) Let the two angles be x and 2x. Look at the figure above. Now, SP || RQ and PR is a transversal. ∴ ∠a = 30° [Using (ii)] Question 4. 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. The common point is called its vertex of the angle. (a) vertically opposite angles Solution: Same, Question 48. Now, EF || GH and AB is a transversal. If a quadrilateral has three angles of equal measure, then the fourth angle must be a right angle. a and b are on the opposite side of transversal l. (a) Since, POR is a straight line. ∠APS + ∠PSC = 130° + 50° = 180° and b = 132° [Vertically opposite angles] (i) Every parallelogram is a rhombus. A protractor is used to measure angle. In the given figure, show that (vii) The diagonals of a trapezium, divide each other into proportional segments. State with reasons whether the following statements are ‘true’ or ‘false’. A full rotation consists of four right angles. ⇒ 120° + ∠x – 180° [Using (1)] Thus, the required angle is 119°. Solution: Hence ∠ACD and ∠DCB are complementary angles. Two angles are vertical. Thus, one angle is 44° and other is 46°. Now, SOT is a straight line In the given figure, lines PQ and ST intersect at O. Which player has the best kicking angle? If two angles have a common vertex and their arms form opposite rays (see figure). One angle is 30 degrees less than the other. The two vertically opposite angles are always equal. Can two acute angles form a pair of supplementary angles? (ii) EF is a straight line. ⇒ z + 36° = 180° ⇒ z = 180° – 36° = 144°, Question 31. Thus, both the angles are of 83°. Question 42. If angle with measure x and y form a complementary ... answer as true or false. In the figure below, ABC is a geometrical shape called Triangle (we will know more about triangle in other article). If ∠AOE = 30° and ∠DOB = 40° (see figure), find ∠COF. Solution: ∴ ∠QOR = 3y = 3× 30° = 90°, Question 15. ⇒ ∠RSC = 180° – 65° = 115° And we know that vertically opposite angles are equal. ∴ ∠1 + ∠x = 180° [Co-interior angles] (a) pair of complementary angles Facts about vertical angles ∴ ∠QRS – ∠TSR = 85° ———- (ii) [Using (i)] [Alternate interior angles] (b) two pairs of supplementary angles. Thus, ∠ABC = 60° and ∠CDE = 120°, Question 100. In the given figure, PQ || ST. Then, the value of x + y is Answer: (b) equal. The value of a is \(\Rightarrow x=\frac{180^{\circ}}{3}=60^{\circ}\) Any angle can have adjacent angles on its both sides. Solution: sum of interior angles on the same side of a transversal is _________ ∴ ∠3=68° ——– (i) [Corresponding angles] (c) a is false and b is true (ii). ⇒ 3a – b = 180 – 2a – b ∠3 + ∠8 = 180° ——– (ii) [Co-interior angles] ⇒ 50° + ∠BCD = 180° Solution: (d) 154° Therefore, B will be less than 45°. (c) Draw a line L.M passing through T such that LM || QP || SR. = 264° + 132° = 396°. (b) 90° ∴ x + y = 90° ———(i) [Angles are complementary] ⇒ 2∠ABP = 180° – 46° = 134 ⇒ ∠3 – 180° – 105° = 75° [From (ii) part] We know that the sum of the measures of the complementary angles is 90° Can two obtuse angles form a … Let one angle be 2x + 1, then the other angle is 2x + 3. ⇒ x + x = 180° [∵Angles are supplementary] (c) ∠3 + ∠8 = 180° An angle that is less than 90 degrees is called an acute angle. Question 58. Thus, the greater angle is 100°. Angle e is vertically opposite angle b . (d) making a linear pair Measures (in degrees) of two complementary angles are two consecutive even integers. Question 97. (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. (e) Since, POQ is a straight line. NCERT Exemplar Class 7 Maths Chapter 5 Lines and Angles are part of NCERT Exemplar Class 7 Maths. A protractor has dual scales. Outer scale is marked in degrees from 0 to 180 from left to right. (i) Since, PQ || UT and PT is a transversal. Let one angle be 2x and the other angle be 2x + 2. ⇒ x = 28° Solution: ⇒ 60° + ∠2 = 180° [Using (ii)] We have, (b) PQ is a straight line. ⇒ ∠2 = 180° – (2a+ b)° ——– (ii) [∵ ∠1 = (2a + b)° (given)] (a) interior angles on the same side of the transversal 180° then they are congruent to each other and formed by parallel l. 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**vertically opposite angles are always equal true or false 2021**