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Q.

State whether the following statement is true or false.

If the two angles that make up a pair of linear angles are equal then each of these angles is of measure $90 ° .$

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a

True

b

False

answer is A.

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Detailed Solution

It is given that the two angles that make up a pair of linear angles are equal.
We know that two adjacent angles that have non-common sides that form opposite rays are called a linear pair.
A linear pair of angles are those angles that are adjacent and supplementary.
Let’s assume two angles of equal measure, then measure of the angles forming a linear pair to be

x

and

x

respectively.

∴ x + x = 180 ° ⇒ 2 x = 180 ° ⇒ x = 90 °

Therefore, if the two angles that make up a pair of linear angles are equal then each of these angles is of measure

90 ° .

Thus, the given statement is true.
Hence, option (1) is correct.

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