15
practice examMultiple Choice

Practice Exam

Question 15 • TPS EdX Geometry

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

Answer
A
Each angle measure is equal to the measure of the arc it intercepts.
B
The measures of each pair of opposite arcs sum to 180 degrees .
C
The sum of the measures of each pair of vertical angles is equal to the sum of the measures of the intercepted arcs.
D
Each arc measure is equal to one-half the sum of the vertical angles that intercept the arc.

Explanation

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. The two vertical angles have equal measures, so their sum equals the sum of those two intercepted arc measures. Thus, the statement that the sum of each pair of vertical angles equals the sum of the intercepted arcs must be true.

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