Step-by-step explanation:
To find the measure of the arc, we can use the formula:
\[ \text{Measure of the arc} = \frac{\text{Central angle}}{360^\circ} \times 2\pi r \]
Where:
- Central angle is the angle formed by the radii at the endpoints of the arc.
- \( r \) is the radius of the circle.
For the first question:
Given that the central angle \( \angle SU \) is \( 98^\circ \), we can calculate the measure of the arc using the formula above. Since the radius is not given, we can assume it to be 1 for simplicity. Then,
\[ \text{Measure of the arc } \overline{SU} = \frac{98^\circ}{360^\circ} \times 2\pi \times 1 \]
\[ = \frac{98}{360} \times 2\pi \]
\[ = \frac{49}{180} \pi \]
So, the measure of the arc \( \overline{SU} \) is \( \frac{49}{180} \pi \).
For the second question:
Given that the measures of the arcs are \( 16x+8 \) and \( 13x+4 \), and the central angle \( \angle SU \) is \( 98^\circ \), we can set up an equation using the formula above:
\[ \frac{16x+8}{360} \times 2\pi r + \frac{13x+4}{360} \times 2\pi r = 98^\circ \]
Solving this equation will give us the value of \( x \), which can then be used to find the measures of the arcs \( \overline{MSU} \) and \( \overline{UT} \).
