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Question
Two adjacent angles are equal. Is it necessary that each of these angles will be a right angle? Justify your answer.
Solution
We know,
Two angles are said to be adjacent, if they have a common vertex, a common arm, and their non-common arms are situated on different sides of the common arm.
Also, we know that the linear pair axiom states that, if a ray stands on a line, then the sum of the two adjacent angles so formed is 180°.
It is given to us that the two adjacent angles are equal. Let us assume each of the adjacent angles measures x.
We know that the sum of two adjacent angles is 180°.
⇒ x + x = 180°
⇒ 2x = 180°
⇒ x = 90°
Thus, each of the adjacent angle is 90°.
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