Given:
Measure of arc MF = 42 degrees
Measure of arc NH = 132 degrees
Let's find the measure of angle C.
To find the measure of angle C, apply the arc and secant relationship:
[tex]m\angle C=\frac{far\text{ arc - near arc}}{2}[/tex]Where:
Far arc = arc NH = 132 degrees
Near arc = arc MF = 42 degrees
Thus, we have:
[tex]\begin{gathered} m\angle C=\frac{132-42}{2} \\ \\ m\angle C=\frac{90}{2} \\ \\ m\angle C=45^0 \end{gathered}[/tex]Therefore, the measure of angle C is 45 degrees.
ANSWER:
45 degrees.