Question

In the given figure, AOB is a straight line. Find the value of x and also find the measure of:-
(1) $\angle AOP$
(2) $\angle BOP$

Answer 1

$\angle AOP=x+{30}^{\circ }\angle BOP=x-{30}^{\circ }But\angle AOP+\angle BOP={180}^{\circ }(\because \angle AOBisastraightangle)\Rightarrow x+{30}^{\circ }+x-{30}^{\circ }={180}^{\circ }\Rightarrow 2x={180}^{\circ }\Rightarrow x={90}^{\circ }\left(1\right)\angle AOP=x+{30}^{\circ }={90}^{\circ }+{30}^{\circ }={120}^{\circ }\left(2\right)\angle BOP=x-{30}^{\circ }={90}^{\circ }-{30}^{\circ }={60}^{\circ }$