Question

Hi there, I am having some trouble identifying the last three parts of this question.

Answer 1

Solution

The angle bisector theorem

We can deduce that ;

$\begin{gathered} \angle PNQ=\angle QNM \\ \\ \angle QNM=\frac{1}{2}\angle PNM \end{gathered}$

The line NQ bisects angle PNM

To find measure of angle PNM , we will use sum of angles in a triangle = 180 degrees

$\begin{gathered} P+\angle PNM+M=180^0 \\ 62+\angle PNM+36=180 \\ \angle PNM=180-36-62 \\ \angle PNM=82^0 \end{gathered}$$\begin{gathered} \angle QNM=\frac{1}{2}PNM \\ =\frac{1}{2}\times82 \\ \\ =41^0 \end{gathered}$