Question

Question 117

In the given figure, find the measures of $\angle PON$ and $\angle NPO$

Answer 1

In $\Delta LOM$,
$\angle OLM+\angle OML+\angle LOM={180}^{\circ }$ [angle sum property of a triangle]
$\Rightarrow {70}^{\circ }+{20}^{\circ }+\angle LOM={180}^{\circ }\Rightarrow {90}^{\circ }+\angle LOM={180}^{\circ }\Rightarrow \angle LOM={180}^{\circ }-{90}^{\circ }={90}^{\circ }Also,\angle PON={90}^{\circ }$
[since, vertically opposite angles are equal]
In $\Delta PON$, $\angle PON+\angle NPO+\angle ONP={180}^{\circ }$ [angle sum property of a triangle]
$\Rightarrow {90}^{\circ }+\angle NPO+{70}^{\circ }={180}^{\circ }\Rightarrow \angle NPO={180}^{\circ }-{160}^{\circ }={20}^{\circ }$