Question

find the arc measure where the ? is

Explanation:

Step1: Recall intersecting chords theorem

The measure of an angle formed by two intersecting chords is half the sum of the measures of the intercepted arcs. The formula is:
$$m\angle AS T = \frac{1}{2}(m\overset{\frown}{VT} + m\overset{\frown}{U T})$$

Step2: Substitute known values

We know $m\angle AS T = 120^\circ$, $m\overset{\frown}{VT} = 60^\circ$. Let $m\overset{\frown}{UT} = x$.
$$120 = \frac{1}{2}(60 + x)$$

Step3: Solve for $x$

Multiply both sides by 2:
$$240 = 60 + x$$
Subtract 60 from both sides:
$$x = 240 - 60 = 180$$

Answer:

$180^\circ$