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Question

Which of the following statements are true (T)  and which are false (F)?

(i) Angles forming a linear pair are supplementary.
(ii) If two adjacent angles are equal, then each angle measures 90°.
(iii) Angles forming a linear pair can both be acute angles.
(iv) If angles forming a linear pair are equal, then each of these angles is of measure 90°.


Solution

(i) True

As the sum of the angles forming a linear pair is.

(ii) False

As the statement is incomplete in itself.

(iii) False

Let us assume one of the angle in a linear pair be; such that ,that is, an acute angle.

Therefore, the other angle in the linear pair becomes, which clearly cannot be acute.

(iv) True

Let one of the angle in the linear pair be. Then, other angle also becomes equal to.

Therefore, by the definition of linear pair, we get:

.

Hence, if angles forming a linear pair are equal, then each of these angles is of measure.


Mathematics
RD Sharma (2017)
Standard IX

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