Question

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

Answer 1

The angle bisector theorem

We can deduce that ;

`\begin{gathered} \angle PNQ=\angle QNM \\ \\ \angle QNM=(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=(1)/(2)PNM \\ =(1)/(2)*82 \\ \\ =41^0 \end{gathered}`