Question

The angle between the bisectors of two adjacent supplementary angles is a right angle.

• A. True
• B. False

Answer 1

The correct option is A

True

Let $\angle A$ and $\angle B$ be adjacent supplementary angles as shown in the figure.


Then, $\angle A+\angle B={180}^{\circ }$
The bisectors of the angles are drawn. We have to find $\angle 1+\angle 2$.
$\angle 1+\angle 2=(\frac{\angle A}{2}+\frac{\angle B}{2})$
$=\frac{180}{2}={90}^{\circ }$
Hence, the angle between the bisectors of adjacent supplementary angles is ${90}^{\circ }$.