Chapter 5.1, Problem 25PPS

To determine

To find: The value of $\angle PQS$ .

Answer to Problem 25PPS

The value is $\angle PQS=42$ .

Explanation of Solution

Given information:

The given figure is

  

Calculation:

Since $SP=SR$ and $SP\perp QP$ , and $SR\perp QR$ then $QS$ is a bisector of angle $\angle PQR$ .

Use definition of angle bisector theorem to calculate $\angle RQS$ .

  $\begin{array}{l}\angle RQS+90+48=180\\ \angle RQS=180-38\\ \angle RQS=42\end{array}$

As we know $\angle RQS=\angle PQS$ then $\angle PQS=42$

Therefore, the value is $\angle PQS=42$ .