Question

In the given figure, ray $OC$ is the bisector of $\angle AOB$ and $OD$ is the ray opposite $OC$. Show that $\angle AOD=\angle BOD$

Answer 1

Since $DOC$ is a straight line, we have:
$\angle BOD+\angle COB={180}^{\circ }$ .........(1)
$\angle AOC+\angle AOD={180}^{\circ }$ ..........(2)
From (1) and (2), we get:
$\angle BOD+\angle COB=\angle AOC+\angle AOD$
Also,$\angle COB=\angle AOC$ [Since $OC$ is a bisector of $\angle AOB$]
$\therefore \angle AOD=\angle BOD$