### Home > GC > Chapter 11 > Lesson 11.2.3 > Problem 11-97

11-97.

**Examine** the diagram at right.

Solve for

, , and Look above at the image of the circle.

because they are supplementary angles. Use the Triangle Angle Sum Theorem to solve for

.

Compare the result for

withand . Is there a relationship? Since

*c*is equal to, the measure of the vertical angles ( ) is the average of the measure of the two arcs that the vertical angles intercept.