Chapter 10.7, Problem 2PSA

To determine

Find angle $m\angle Randm\angle P$ .

Answer to Problem 2PSA

  $m\angle R=105°,m\angle P=75°$

Explanation of Solution

Given information:

  

  $PS=110°,PQ=100°$

Calculation:

It is given ,

  $PS=110°,PQ=100°$

  $\begin{array}{l}m\angle R=\frac{1}{2}m\stackrel{}{\overbrace{SP}}+m\stackrel{}{\overbrace{PQ}}\left[inscribedangletheorem\right]\\ m\angle R=\frac{1}{2}\left(110+100\right)\\ m\angle R=105°\\ m\angle R+m\angle P=180°\left[inscribedquadrilateraloppositeanglesare\sup p\mathrm{l}ementry\right]\\ 105°+m\angle P=180°\\ m\angle P=180°-105°=75°\end{array}$

Hence, $m\angle R=105°,m\angle P=75°$ .