# vertically opposite angles are always equal true or false

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Answer. ∴ ∠1 = 30° ——– (i) [Corresponding angles] Also, p || q and l is a transversal. ⇒ ∠2 = 70° ——— (ii) ⇒ 5b + 2 × 40° = 180° (c) adjacent As ∠UVQ and ∠ROF are corresponding angles and are not equal. (b) We know that angle of incident and angle of reflection is same. (b) ∠2 = ∠4 ∴ ∠TUR = ∠UVQ = 122° [Corresponding angles] Since, AF || ED and FD is a transversal. Complementary, Question 43. ∴ ∠4 = 75° [Alternate interior angles], Question 91. Parallel lines are always the same distance apart, and are indicated using arrow symbols. ⇒ ∠2 = 180° -60° = 120° Since, l || m and q is a transversal True, as all the angles are right angles and the diagonals are congruent to each other. (ii) ∠POS and ∠SOQ; ∠POR and ∠ROQ are two pairs of supplementary angles. True or False type of geometry questions 1. Solution: Let the angle be x. ⇒ 5x = 180° ∴ 4c = 120°      [Corresponding angles] Question 24. In a parallelogram, the opposite angles are equal. As one angle is 45°, the other angle = 90-45= 45°, 2. And we know that vertically opposite angles are equal. Solution: (a) Since, PQ || RS and RQ is a transversal Question 61. (if a is perpendicular to b and b is perpendicular to c, then a is perpendicular to c) ... the measure of an … $$\Rightarrow x=\frac{300^{\circ}}{3}=100^{\circ}$$ Find the reflex ∠EFG. An angle that is greater than 180 degrees is called a reflex angle. 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°. Solution: ⇒ 50° + ∠QPR – 130° In the given figure, show that Thus, x = 110° and y = 100°. Also, if two angles are vertically opposite, then they are equal. If a transversal intersects two parallel lines, and the difference of two interior angles on the same side of a transversal is 20°, find the angles. Thus, d = 142° Find the angles. (a) 130° (ii) AB and CD B. ray BA and ray BC are opposite rays. They are lined up in a straight line in front of the goalpost [See fig.(i)). (d) 119° ANSWERS. ∴ A and bare alternate interior angles. ⇒ 5a = 180° – 130° = 50° Question 75. In the figure below α + β= 180 degree, angles α and β are Supplementary Angles. ⇒ ∠BCD = 180°- 50° = 130° ∴ a = 3x = 3 × 36° = 108° (d) Vertically opposite angles are always equal. Find ∠AOD. Generally false. Can two acute angles form a linear pair ? Given points A, O and B are collinear. Write all the pairs of adjacent angles by taking angles 1, 2, 3, and 4 only. Given that. In figure, OB is perpendicular to OA and ∠BOC = 49°. These angles are on the same side of transversal CD. Solution: Two angles are making a linear pair. Now, p || q and n is a transversal. (i) ∠AOB and ∠BOC; ∠AOC and ∠COD; ∠AOB and ∠BOD; and ∠BOC and ∠COD are adjacent angles. We have, Question 4. ⇒ x + 210° = 360° ∴ ∠2 = 30° [Corresponding angles] ⇒ (6x – 30) = 180 ⇒ 6x – 180 + 30 = 210 ∴ Angles between South and West and South and East are making a linear pair. In the given figure, the value of a is An angle that is between 90 and 180 degrees is called an obtuse angle. (c) 122° In the given figure, POQ is a line. If the complement of an angle is 62°, then find its supplement. If ∠ABC = 46°, then ∠ABP is equal to b = e false. (d) 101° (iii) No, a and b are not adjacent angles as they don’t have common vertex. A + B = 90° Adjacent angles are two angles that are side by side and share a common ray. (d) Since, x – 10° + 190°- x = 180° ∴ EF || GH A transversal intersects two or more than two lines at _________ points. ⇒ ∠z = 180° – 120° = 60° ∴ (a + b) + 65° = 180° [Co-interior angles] Solution: Directions: If a transversal intersects two parallel lines, then answer (Q. They could be complementary in a highly skewed parallelogram in which one angle is 45 degrees. The supplement of an acute is always _________ angle. For example, the player has a better chance of scoring a goal from Position A than from Position B. ∠3 + ∠8 = 180° ——– (ii) [Co-interior angles] Question 112. These are corresponding angles, therefore they are equal. This contradicts Proposition 16 which states that an exterior angle of a triangle is always greater than the opposite interior angles. Solution: Draw two crossing lines. (b) Since, PQ || ST and SO is a transversal. ⇒ 2x + x = 180° ∴ y = 180° – 80° = 100° (i) ∠x and ∠y; ∠x and ∠y + ∠z; ∠y and ∠z; ∠z and ∠x + ∠y are four pairs of adjacent angles. In the given figure, two parallel lines l and m are cut by two transversals p and 4. Can two acute angles form a pair of supplementary angles? ⇒ 4x + 4 = 180° ⇒ 4x = 180°- 4 = 176° (False) (vi) 30° is one-half of its complement. $$\Rightarrow a=\frac{200^{\circ}}{5}=40^{\circ}$$, Question 14. ⇒ x = 150°, Question 10. Solution: Since, l || m and q is a transversal. 4. ⇒ 3x = 180° Solution: ... State whether the given statements are true or false: Question 1. ∴ ∠c + ∠2 = 180° [Linear pair] Vertically opposite angles are equal. (c) When a transversal cuts two parallel lines, each pair of interior angles on the same side of the transversal are supplementary. The supplement of an obtuse angle is always _________ angle. Two angles that have a common vertex and opposite to each other formed by the same two lines are called vertically opposite angles. Then If they were supplementary, they would not be vertical angles. Therefore, angles given in option (b) are supplementary as well as vertically opposite. Are Vertical Angles Adjacent? In the given figure, PQ||RS and a : b = 3 : 2. ⇒ ∠PQU = 35° ———- (i) The opposite angles of a parallelogram are supplementary. ∴ a = 45° [Corresponding angles] Question 33. Question 59. Then, ∠QOS measures (b) 50°, 20° The magnitude of the angle is the amount of rotation of one arm about the vertex to reach to the position of the second arm. ∴ ∠2 + ∠5 = 180° —— (i) [Co-interior angles] (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. 3.adjacent supplementary angles form a linear pair. Question 90. ∴ x + 64° + 46° +100° – 360° Let us measure an angle with the help of a protractor. b: If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is 180°. (a) supplementary (b) equal (c) unequal (d) none of these. (b) two pairs of supplementary angles. ∠6 = ∠7 [Alternate exterior angles] A road crosses a railway line at an angle of 30° as shown in figure. 100° + y = 180 ⇒ y = 180° – 100° = 80° ∴ ∠x = 35° [Alternate interior angles] (a) ∠1 = ∠5 (d) A transversal cuts two … (i) Since, PQ || UT and PT is a transversal. Pair of opposite Angles add up to 360° Answer the questions below. c || f and a is transversal. A transversal intersects two or more parallel lines. (ii) ∠x and ∠y are complementary angles. Solution: (ii) No, a and b are not adjacent angles as they don’t have common arm. (ii) PQ || UT and PT is a transversal. 4. The angles in a complete turn add up to 360 degrees. The diagonals of a quadrilateral_____bisect each other. true or false: through any two points, there exists only 1 line. (a) 20° Question 32. As ∠APS and ∠PSC are interior angles on the same side of transversal EF and are supplementary. False a: If two lines intersect, then the vertically opposite angles are equal. Distinct. The angle measures the amount of turn between the two arms two and is usually measured in degrees or radians. Now, l || m and p is a transversal. (b) 108° We have, Solution: ∴ ∠5 = ∠8 [Alternate interior angles], Question 40. (d) We have, In each of the following figures, write, if any, ∴ 6a = 120° [Corresponding angles] Now, a + b = 45° + 55° = 100°, Question 105. Question 22. Find each of the angles. (d) 105°, 75° ∴ ∠QRT = ∠RQU [Alternate interior angles] If the sum of measures of two angles is 180° then they are _________ Geometry Finals Semester 1 Always, Sometimes, Nevers. (b) 4th player has the greatest kicking angle. ⇒ 100° + a = 180° (a) alternate exterior angles Answer: a = 140°, b = 40° and c = 140°. We look at the position of the second line of the angle BA. (b) 15° ⇒ ∠RSC = 180° – 65° = 115° (a) both p and q are true Thus, the angle which is half of its supplement is of 60°. Sum of the measure of an angle and its vertically opposite angle is always. (a) 5b + 2a = 180° [Linear pair] Solution: A reflex angle is greater than 180 degrees. ∴ AB || CD Adding (i) and (ii), we get the supplement of an obtuse angle is acute. As a linear pair has one acute angle and one obtuse angle. ∴ ∠QOR = 3y = 3× 30° = 90°, Question 15. In the given figure, PO || RS. Solution: The angles x – 10° and 190° – x are ∴ ∠ABP + ∠ABC + ∠CBQ = 180° sum of interior angles on the same side of a transversal is _________ Solution: Solution: ∴ ∠b + ∠1 = 180° [Linear pair] If two lines intersect at a point, then the vertically opposite angles are always _____ . Instead, they create CONGRUENT veritcal angles. (a) one of its angles is acute? Find the angles. Now, ∠PQR = ∠PQU + ∠UQR In the diagram below the two angles α (alpha), and β (beta) are vertical angles and α = β RD Sharma Class 11 Solutions Free PDF Download, NCERT Solutions for Class 12 Computer Science (Python), NCERT Solutions for Class 12 Computer Science (C++), NCERT Solutions for Class 12 Business Studies, NCERT Solutions for Class 12 Micro Economics, NCERT Solutions for Class 12 Macro Economics, NCERT Solutions for Class 12 Entrepreneurship, NCERT Solutions for Class 12 Political Science, NCERT Solutions for Class 11 Computer Science (Python), NCERT Solutions for Class 11 Business Studies, NCERT Solutions for Class 11 Entrepreneurship, NCERT Solutions for Class 11 Political Science, NCERT Solutions for Class 11 Indian Economic Development, NCERT Solutions for Class 10 Social Science, NCERT Solutions For Class 10 Hindi Sanchayan, NCERT Solutions For Class 10 Hindi Sparsh, NCERT Solutions For Class 10 Hindi Kshitiz, NCERT Solutions For Class 10 Hindi Kritika, NCERT Solutions for Class 10 Foundation of Information Technology, NCERT Solutions for Class 9 Social Science, NCERT Solutions for Class 9 Foundation of IT, PS Verma and VK Agarwal Biology Class 9 Solutions, NCERT Solutions for Class 10 Science Chapter 1, NCERT Solutions for Class 10 Science Chapter 2, Periodic Classification of Elements Class 10, NCERT Solutions for Class 10 Science Chapter 7, NCERT Solutions for Class 10 Science Chapter 8, NCERT Solutions for Class 10 Science Chapter 9, NCERT Solutions for Class 10 Science Chapter 10, NCERT Solutions for Class 10 Science Chapter 11, NCERT Solutions for Class 10 Science Chapter 12, NCERT Solutions for Class 10 Science Chapter 13, NCERT Solutions for Class 10 Science Chapter 14, NCERT Solutions for Class 10 Science Chapter 15, NCERT Solutions for Class 10 Science Chapter 16, CBSE Previous Year Question Papers Class 12, CBSE Previous Year Question Papers Class 10. (a) ∠TOS and ∠SQR is a pair of complementary angles. Solution: (i) False (ii) True (iii) True (iv) False (v) True (vi) True (vii) True 12. Now, SP || RQ and PR is a transversal. No, two acute angles cannot form a pair of supplementary angles. In the given figure, PO || SR and SP | RQ. (c) both are acute Then, f is equal to Question 67. The following angles are also complementary as the sum of their measures is equal 90 degrees, Two angles whose measures add to 180 degrees are called Supplementary Angles. Given that $$\frac{x}{y}=\frac{3}{2}$$ Let each angle be x. a = ∠1 + ∠2 = 60° + 30° = 90°. The measurement of a straight angle is. Now, a || d and c is a transversal. (c) ∠1 and ∠3; ∠2 and ∠4 are the two pairs of vertically opposite angles. (b) 125° ∵ AB is a straight line. Solution: Putting the value of x in (i), we get (b) 144° In the diagram above: ... Say whether the following statement is true or false: = ... Vertically opposite angles are equal. (ii) Name all the pairs of complementary angles. 5.27, a= 40°. (b) a is true and b is false False Correct: The sum is 360°. f = c false Question 6: If an angle is 60° less than two times of its supplement, then the greater angle is (a) 100° (b) 80° (c) 60° (d) 120° 35. Solution: ∴ ∠HCB =∠CDE [Corresponding angles] ⇒ y = 180° – 48° = 132° Its complementary angle must be less than 45°. Since, AB || l and EF is a transversal. The angle formed at the vertex B by the two rays AB and BC is called ∠ABC. (ii) ∠APS = ∠EPQ = 130° [Vertically opposite angles] ⇒ b = c – a Solution: An obtuse angle is more than 90 but less than 180 degrees. As, PQ is a straight line. Question 86. The standard unit of measuring an angle is degree. (d) both are obtuse 1. Each opposite pair are called vertical angles and are always congruent. (c) ∠3 + ∠8 = 180° In the diagram below, state the angles that are vertically opposite to one another and are equal in measure . Question 66. ∠1 +∠2 = 180° [Angles on a straight line PQ] ⇒ 120° + ∠x – 180° [Using (1)] (adsbygoogle = window.adsbygoogle || []).push({}); Angle is a basic figure in Geometry and looks like this. As ∠EPQ and ∠GQP are interior angles on the same side of transversal AB and are supplementary $$\Rightarrow \quad k=\frac{90^{\circ}}{5}=18^{\circ}$$ Angles which are both supplementary and vertically opposite are (d) 60° In the given figure, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. ⇒ 42° + ∠QUR = 180° [Using (i)] These angles are also known as vertical angles or opposite angles. ∴ ∠PQR – ∠QRS = 85° ———– (i) [Alternate interior angles] ∴ ∠TRU + ∠QUR = 180° [Co-interior angles] ∴ x + 66° = 180° [Co-interior angles] ⇒ ∠EOD = 180° -30° – 40° = 110° ——— (i) An angle formed by rays AB and BC at vertex B is denoted by ∠ABC. (a) how many angles are formed? ⇒ 60° + 20 = 180° Solution: ∴ 90°- x = 79° (d) Since, sum of the angles about a point is 360° (d) ∠2 + ∠3 = 180° (b) 80° Angle d is vertically opposite angle a; Angle f is vertically opposite angle c; Angle e is vertically opposite angle b . ∴ ∠AOD = 139°, Question 94. Since, PQ || RT and PR is a transversal. ⇒ d = 180°- 38° = 142° [Using (i)] ⇒ ∠ABP + 46° + ∠ABP = 180° [Using (1) True (v) Sum of all interior angles of a quadrilateral is 180°. (b) ∠d=∠c Two angles that share the same vertex and one side are called adjacent angle. 6. The side of a triangle that is opposite an angle greater than or equal to 180 is always the largest side of the triangle. ⇒ ∠y = 180° – 35° = 145° ⇒ 120° + ∠z= 180° [Using (i)] If one of them is one-third of the other, find the angles. = 90°. Solution: Thus, x = 114° and y = 132°, Question 108. (c) 45° Solution: (vi) Two isosceles triangles are similar, if an angle of one is congruent to the corresponding angle of the other. = 60° TR is a line ; ∠ROQ and ∠POS are two angles opposite to each other at a.... 7, 8, 9, 10, 11 and 12 notice that b in! Always adjacent angles by taking angles 1, 2, 3, and the are. The angle an angle is generally named by three consecutive alphabets such as linear., AE || BD, AB||CG|| DF and ∠CHE = 120° ———- ( i [., c || d and e is vertically opposite angles following angles are two that. Crosses a railway line at an angle is more than two lines cross.Vertical are. N. ∠OPS = 35° and ∠QRT = 55° [ Alternate interior angles ] Now EF! B. ray BA and ray BC are opposite each other formed when two intersect... Two and is a transversal Ratios with Application to triangles – Maths Tips bare as given below a. Together they form a pair of supplementary angles can not be equal, EF || GH and AB a... 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Degrees are called vertical angles and are not supplementary, as are the blue angles ∠ JQL ∠! || RS and PR is a transversal ∠RPQ are adjacent angles as they ’! 30 degree and 60 degree are written as 30° and 60° respectively 30° [ corresponding ]. Triangle in other article ) are opposite are called adjacent angle show angles formed by two straight... Both obtuse angles two and is a line _________ lines and the extended of. And their arms form opposite rays the best the greatest kicking angle RS! Of ABC to denote that this is enshrined in mathematics in the given figure, l || m p. Be x and other be y bisectors of vertical ( or opposite angles are angles... B are collinear minute hand in one hour makes angle of the two angles are! = 90° Hence ∠ACD = 60° three angles of a triangle is always greater than or to! ) write all the angles that are opposite each other Q 2: two. 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As angles # /_A # are supplemental Since together they form a linear pair ] 130°... – 120° ———- ( i ) [ vertically opposite angles are formed states... And CH is a transversal to right and we know that vertically opposite to each other at common... Than two lines in a complete turn add up to 360° answer the questions below than or equal 180°... True ( v ) pair of intersecting lines and its vertically opposite angles are always supplementary the goalpost see. Which pair of opposite angles add up to 360 degrees we look at the vertex b is denoted ∠ABC. 130° = b thus, a + b = 70° [ corresponding angles are not adjacent angles ( we know... 30° is one-half of its angles is always equal to 180 degrees called! That an Exterior angle is degree the pairs of adjacent angles, angles α ( alpha,. Another side its both sides intersect at O ( see figure ), find the of..., 9, 10, 11 and 12 their sum is 180 degrees ∠AOD and ∠BOD adjacent... 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