Question

In the given figure, $AOB$ is a straight line and the ray $OC$ stands on it.
If $\angle AOC={64}^{\circ }$ and $\angle BOC=x^{\circ },$ find the value of $x.$

Answer 1

By linear pair property:

$\angle AOC+\angle COB={180}^{\circ }$

$\Rightarrow {64}^{\circ }+\angle COB={180}^{\circ }$

$\Rightarrow x^{\circ }={180}^{\circ }-{64}^{\circ }={116}^{\circ }$ [$\because \angle COB=x^{\circ }$]
$\therefore x={116}^{\circ }$