Chapter 3.7, Problem 12PSB

a.

To determine

The measurement of $\angle PSQ$

Answer to Problem 12PSB

The measurement of $\angle PSQ$ = ${45}^{\circ }$

Explanation of Solution

Given: $\overline{PS}\perp \overline{SR}$ and $\angle P={36}^{\circ }$

Concept used: Here, we are using the concept of angle bisector theorem

Calculation: Here, OS bisects the $\angle PSR$ because OS is radius of circle.

So that, $\angle PSQ={45}^{\circ }$

Conclusion: Hence, the measurement of $\angle PSQ$ = ${45}^{\circ }$

b.

To determine

The measurement of $\angle R$

Answer to Problem 12PSB

The measurement of $\angle R={54}^{\circ }$

Explanation of Solution

Given: $\overline{PS}\perp \overline{SR}$ and $\angle P={36}^{\circ }$

Concept used: Here, we are using the concept of linear angle theorem

Calculation: Here, $\overline{PS}\perp \overline{SR}$ and $\angle P={36}^{\circ }$

So, $\angle P+\angle S+\angle R={180}^{\circ }$

  →${36}^{\circ }+{90}^{\circ }+\angle R={180}^{\circ }$

  →$\angle R={180}^{\circ }-{126}^{\circ }$

  →$\angle R={54}^{\circ }$

Conclusion: Hence, the measurement of $\angle R={54}^{\circ }$