what is msu?\n49°\n77°\n98°\n161°

Answer:

C. $98^{\circ}$

Explanation:

Step1: Recall the secant - secant angle formula

The measure of an angle formed by two secants drawn from an external point to a circle is given by $\angle T=\frac{1}{2}(\text{major arc}-\text{minor arc})$. Let the measure of arc $SU$ be $x$ and the measure of arc $RU$ be $y$. We know that the measure of the whole - circle is $360^{\circ}$, and if we assume the measure of arc $RS = 119^{\circ}$, then $y=360^{\circ}-119^{\circ}-x=241^{\circ}-x$. Also, $\angle T = 21^{\circ}$.

Step2: Apply the formula

Using the formula $\angle T=\frac{1}{2}(y - x)$, substitute $\angle T = 21^{\circ}$ and $y=241^{\circ}-x$ into it. We get $21^{\circ}=\frac{1}{2}((241^{\circ}-x)-x)$.

Step3: Solve the equation

First, multiply both sides of the equation $21^{\circ}=\frac{1}{2}(241^{\circ}-2x)$ by 2: $42^{\circ}=241^{\circ}-2x$. Then, add $2x$ to both sides: $2x + 42^{\circ}=241^{\circ}$. Next, subtract $42^{\circ}$ from both sides: $2x=241^{\circ}-42^{\circ}=199^{\circ}$. Finally, divide both sides by 2: $x = 98^{\circ}$. So the measure of arc $SU$ is $98^{\circ}$.