Question

The bisectors of two adjacent supplementary angles are always at

Answer 1

Let two adjacent supplementary angles are $\angle POQ$ and $\angle ROQ$ such that $OA$ and $OB$ are the angle bisectors



$\therefore \angle 1+\angle 2=\frac{1}{2}\angle POR+\frac{1}{2}\angle QOR$

$=\frac{1}{2}(\angle POR+\angle QOR)$

$=\frac{1}{2}\left({180}^{\circ }\right)$

$={90}^{\circ }$

Hence, the bisectors of two adjacent supplementary angles are always at right angle.