Two chords intersect at a point inside a circle that is not the center of the circle. Which statement must be true?

For two chords intersecting inside a circle, an angle’s measure is half the sum of the measures of the arcs intercepted by that angle and its vertical angle. Since vertical angles are equal, their measures add to twice either angle, which equals the sum of those two arc measures. Thus, the sum of each pair of vertical angles equals the sum of the intercepted arcs.

AI-written and checked against the verified answer.