Mathematics
Assertion: The sum of two vertically opposite angles is 162°, then each of the angles is 81°.
Reason: Vertically opposite angles are supplementary.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- Assertion (A) is true but Reason (R) is false.
- Assertion (A) is false but Reason (R) is true.
Lines & Angles
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Answer
Assertion (A) is true but Reason (R) is false.
Explanation
The assertion states that if the sum of two vertically opposite angles is 162°, then each angle is 81°.
When two lines intersect, the vertically opposite angles formed are always equal.
Calculation:
Let each angle be x.
x + x = 162°
2x = 162°
x =
x = 81°
The Assertion is true.
The reason states that "Vertically opposite angles are supplementary."
Vertically opposite angles are equal, but they are only supplementary if the intersecting lines are perpendicular (forming four 90° angles). In a general case, vertically opposite angles are not supplementary.
The Reason is false.
Hence, option 3 is the correct option.
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Related Questions
Write true (T) or false (F) :
(i) An angle whose measure is 90° is called a straight angle.
(ii) The sum of the angles of a linear pair is 180°.
(iii) When two straight lines cut each other, the sum of any two adjacent angles formed is 180°.
(iv) A line which intersects two other lines at their point of intersection is called a transversal.
(v) When two parallel lines are cut by a transversal, then the exterior opposite angles are supplementary.
Mohit has a complex collection of lines drawn in a plane. He studies the angles formed due to the intersection of these lines. It is known that ∠DOH = 90°.
(1) Which of the following is a pair of vertically opposite angles ?
- ∠AOC, ∠BOG
- ∠BOG, ∠BOD
- ∠COE, ∠FOH
- ∠EOG, ∠FOH
(2) Which of the following is a pair of perpendicular lines ?
- AB, CD
- CD, GH
- AB, EF
- EF, GH
(3) Which of the following is a pair of complementary angles ?
- ∠AOC, ∠COE
- ∠COE, ∠EOG
- ∠EOG, ∠FOH
- ∠COG, ∠DOH
(4) Which of the following is a pair of supplementary angles ?
- ∠COE, ∠DOF
- ∠BOF, ∠AOH
- ∠AOE, ∠BOE
- ∠AOD, ∠BOG
Assertion: Two angles making a linear pair are always supplementary.
Reason: A pair of adjacent angles is said to be a linear pair, if these angles have one arm common and other arms as opposite rays.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- Assertion (A) is true but Reason (R) is false.
- Assertion (A) is false but Reason (R) is true.
Assertion: In the figure l || m, AD || BC and ∠A = 40°. The measure of ∠BCD is 140°.
Reason: If two parallel lines are cut by a transversal, then the pair of corresponding angles are equal and the co-interior angles are supplementary.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- Assertion (A) is true but Reason (R) is false.
- Assertion (A) is false but Reason (R) is true.