Question

Point B is the center of a circle, and AC is a diameter of the circle. Point D is a point on the circle different from A and C. If angle BDA = 20 degrees, what is the measure of angle CBD? Answer choices: a) 70 degrees b) 20 degrees c) 120 degrees d) 140 degrees e) 40 degrees

Answer 1

BA and BD are radii of the circle, so triangle ABD is isosceles. Then angles BDA and BAD are congruent, and the remaining (central) angle ABD has measure

$m\angle ABD=(180-2\cdot20)^\circ=140^\circ$

Angles ABD and CBD are supplementary, so

$m\angle CBD=(180-140)^\circ=40^\circ$

and the answer is E.