Mathematics
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.
Lines & Angles
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Answer
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Explanation
From the figure,
Consider, l || m and AD is the transversal:
∠ADC = ∠A [alternate interior angles]
∴ ∠ADC = 40°
Now, consider AD || BC and m is a transversal:
∠ADC + ∠BCD = 180° [Co-interior angles]
⇒ 40° + ∠BCD = 180°
⇒ ∠BCD = 180° - 40°
⇒ ∠BCD = 140°
The Assertion is true.
The reason states that if two parallel lines are cut by a transversal:
Corresponding angles are equal.
Co-interior angles are supplementary (180°).
These are fundamental properties of parallel lines.
The Reason is true and it is the correct explanation for how we calculated the value in the Assertion.
Hence, option 1 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: 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.