Question

In circle A, Segment BD is a diameter, and the measure of arc CB is 36°: What is the measure of ∠DBC? 36° 72° 18° 54°

Answer 1

The first step is to find angle D. We would apply the theorem which states that the angle formed by the intersection of two chords on a circle is equal to half the interepted arc. From the information given,

BD and CD are chords

angle formed = D

intercepted arc = arc BC = 36

By applying the theorem,

angle D = 36/2 = 18

Given that BD is the diameter of the circle,

angle C = 90 degrees

Recall, the sum of the angles in a triangle = 180. it means that

angle C = 90 degrees

Thus,

B + C + D = 180

B + 18 + 90 = 180

B + 108 = 180

B = 180 - 108

angle DBC = 72 degrees