Question

what is ( moverarc{su} )?
( circ ) ( 49^circ )
( circ ) ( 77^circ )
( circ ) ( 98^circ )
( circ ) ( 161^circ )

Explanation:

Step1: Recall secant angle theorem

The measure of an angle formed by two secants outside a circle is half the difference of the measures of the intercepted arcs. The formula is:
$$m\angle T = \frac{1}{2}(m\overset{\frown}{RU} - m\overset{\frown}{SU})$$

Step2: Substitute known values

We know $m\angle T=21^\circ$, $m\overset{\frown}{RU}=119^\circ$. Plug into the formula:
$$21^\circ = \frac{1}{2}(119^\circ - m\overset{\frown}{SU})$$

Step3: Solve for $m\overset{\frown}{SU}$

Multiply both sides by 2:
$$42^\circ = 119^\circ - m\overset{\frown}{SU}$$
Rearrange to isolate $m\overset{\frown}{SU}$:
$$m\overset{\frown}{SU} = 119^\circ - 42^\circ$$

Answer:

$\boldsymbol{77^\circ}$ (Option B. $77^\circ$)