Question

find the measure of the angle where the ? is

Explanation:

Step1: Recall intersecting chords angle rule

The measure of an angle formed by two intersecting chords is half the sum of the measures of the intercepted arcs.

Step2: Identify intercepted arcs

The intercepted arcs are $\overset{\frown}{RQ}=175^\circ$ and $\overset{\frown}{SA}=55^\circ$.

Step3: Calculate the angle

$\text{Angle } P = \frac{1}{2} \times (175^\circ + 55^\circ)$
$\text{Angle } P = \frac{1}{2} \times 230^\circ$

Answer:

$115^\circ$