Question

What is the measure of DBE? A. 120 B. 75 C. 45 D. 60

Answer 1

Hi!

The intersecting chords theorem states that when two chords of a circle intersect, they form a pair of vertical angles (in this case angle DBE and ABC), and the measure of those angles (since they're congruent, it's the same) is equal to half of the sum of the two intercepted arcs.

That rule applies here. In this case, the intersecting chords are line AE and DC (you can tell because they end on the circle, and they have two endpoints on it), and the intercepted arcs are arc DE and arc AC, with measures of 45 degrees and 75 degrees (respectively).

So to find the measure of angle DBE (one of the vertical angles), just take the sum of the measures of the two intersected arcs, and then divide by 2. In this case, it's 45 + 75, to get 120 degrees, dividing by 2 gets 60 degrees.

So therefore your answer is 60 degrees, or B.

Hope this helped!