### Home > CCG > Chapter 11 > Lesson 11.2.3 > Problem 11-111

11-111.

In part (c) of problem 11-110, you used the relationship between the segment lengths formed by intersecting chords to find a missing length. But how are the arc measures of two random intersecting chords related? 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 vertical angles ( ) are the average of the two arcs they intercept.