Question

In the following questions (No. 21-28) a statement of Assertion followed by a statementof Reason is given. Choose the correct answer out of the following choices.
1) Assertion (A) Two adjacent angles always form a linear pair.
Reason
(R) In a linear pair of angles two non-common arms are opposite rays.
2)22. Assertion (A): The bisectors of the angles of a linear pair at right angles.

Reason (R)If the sum of two adjacent angles is 180 ^ c , then the non-common armsof the angles are in a straight line.

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Answer 1

Answer:

1) Both A and R are correct and R is the correct exlanation of A.

2) Both A and R are correct but R is not the correct explanation of A.

Answer 2

(1)

Assertion: Two adjacent angles always form a linear pair.

Reason: In a linear pair of angles two non-common arms are opposite rays.

Solution:

A = The assertion is incorrect as it is not compulsory that two adjacent angles always form a linear pair. The sum of two adjacent angles can be more or less than 180°.

R = Two adjacent angles are said to form a linear pair if the sum of the angles is 180°, that is, α + β = 180°, this is only possible when the two non=common arms run opposite to each other. Thus, the reason is correct.

Therefore, the Assertion is incorrect.

(2)

Assertion: The bisectors of the angles of a linear pair at right angles.

Reason: If the sum of two adjacent angles is 180°, then the non-common arms of the angles are in a straight line.

Solution:

A = Bisector of an angle divides the angle into two equal halves. A linear pair is one in which the sum of angles is 180°, so the bisector will divide it into two equal angles, that is, 180/2 (which is equal to 90°). Thus, the assertion is correct that the bisector of the angles of a linear pair bisects it at right angles.

R = If the sum of two adjacent angles is 180°, they form a linear pair. In a linear pair, the two non-common arms run opposite to each other, that is, they form a straight line. Thus, the reason is correct.

Thus, the assertion and reason are correct but the reason is not the correct explanation of the assertion.