Chapter 9, Problem 17CR

To determine

To find: the value of $m\angle PLN$ and $m\angle PNR$ .

Answer to Problem 17CR

  $\begin{array}{l}m\angle PNR=50\\ m\angle PNL=50\end{array}$

Explanation of Solution

Given information:

Given statement,

$\overleftrightarrow{RS}$ is tangent to the circle at $N$ .

If $marcPN=100$

Calculation:

Consider the following diagram:

If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

It is already known that. The measure of an inscribed angle is equal to half the measure of its intercepted arc.

Therefore,

  $\begin{array}{c}m\angle PNL=\frac{1}{2}\left(marcPN\right)\\ =\frac{1}{2}\left(100\right)\\ =50\end{array}$

And $m\angle PNR=50$ .