Question

In the given figure; AOC is a straight line. If $\angle AOB={50}^{\circ },\angle AOE={90}^{\circ }and\angle COD={25}^{\circ }$;find the measure of :
(1) $\angle$BOC
(2) $\angle$EOD

Answer 1

(1) $\angle AOB+\angle BOC={180}^{\circ }$ (Angles lying on a straight line)
$\Rightarrow {50}^{\circ }+\angle BOC={180}^{\circ }\Rightarrow \angle BOC={180}^{\circ }-{50}^{\circ }={130}^{\circ }\Rightarrow \angle BOC={130}^{\circ }\left(2\right)\angle EOD+\angle COD={90}^{\circ }(\because \angle AOE={90}^{\circ })\Rightarrow \angle EOD+{25}^{\circ }={90}^{\circ }\Rightarrow \angle EOD={90}^{\circ }-{25}^{\circ }\Rightarrow \angle EOD={65}^{\circ }$