Chapter 9, Problem 18CR

To determine

The value of the given side and angle.

Answer to Problem 18CR

The required sides are $m\angle PNL$ and $mPL$ are 140 and 110 respectively.

Explanation of Solution

Given:

The figure is given as;

  

The required sides are $m\angle PNL$ and $mPL$ .

If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. It is given that $mPL=110$ .

It is already known that, the measure of an inscribed angle is equal to half the measure of its intercepted arc and if a quadrilateral is inscribed in a circle, then it opposite angles are supplementary.

Then, from the above theorem, $m\angle N=70$ .

So,

  $\begin{array}{c}2m\angle N=m\angle PNL\\ m\angle PNL=2\left(70\right)\\ =140\end{array}$

Therefore, the required sides are $m\angle PNL$ and $mPL$ are 140 and 110 respectively.