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 inside a circle is half the sum of the measures of the intercepted arcs.

Step2: Identify intercepted arcs

The intercepted arcs are $\overset{\frown}{FS}=53^\circ$ and $\overset{\frown}{UT}=175^\circ$.

Step3: Calculate the angle

$$\text{Measure of } \angle V = \frac{1}{2} \times (53^\circ + 175^\circ)$$
$$= \frac{1}{2} \times 228^\circ$$
$$= 114^\circ$$

Answer:

$114^\circ$