Question

Draw a linear pair of angles. Bisect each of the two angles. Verify that the two bisecting rays are perpendicular to each other.

Answer 1

Two angles, which are adjacent and supplementary are called linear pair of angles.
Draw a line $AB$ and mark a point $O$ on it.
When we draw an $\angle AOC$, we also get another angle $BOC$.
Bisect $\angle AOC$ by a compass and a ruler and get the ray $OX$.
Similarly, bisect $\angle BOC$ and get the ray $OY$.

Verification:
$\angle XOY=\angle XOC+\angle COY$
$=\frac{1}{2}\angle AOC+\frac{1}{2}\angle BOC$
$=\frac{1}{2}(\angle AOC+\angle BOC)$

$=\frac{1}{2}\times {180}^{\circ }$ [As$\angle AOC$ and $\angle BOC$ are supplementary angles]

$={90}^{\circ }$

Hence, the two bisecting rays are perpendicular to each other.