Chapter 9, Problem 16CR

To determine

To find: the value of $m\angle PNL$ .

Answer to Problem 16CR

The value of $m\angle PNL=75°$ .

Explanation of Solution

Given information:

Given statement,

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

If $m\angle K=105$

Calculation:

Consider the following diagram:

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

In the referred diagram, the angles $m\angle K$ and $m\angle PNL$ are supplementary angles of each other.

Therefore, the sums of these two angles are $180°$ .

Then,

  $\begin{array}{c}m\angle PNL+m\angle K=180°\\ =180°-105°\\ =75°\\ m\angle PNL=75°\end{array}$

So, the value of $m\angle PNL=75°$ .