, , and using what you know about inscribed angles and the sum of the angles of a triangle.
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
with and . 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.