Question

In circle P, the measure of arc BDC is 260, what is the measure of angle 1?

A. 100
B. 60
C. 50
D. 80

Answer 1

C. 50 deg

Explanation:

m(arc)BDC = 260 deg

Since a full circle has an arc measure of 360 deg, we can find the measure of arc BC.

m(arc)BC = 360 deg - 260 deg = 100 deg

Angle 1 is formed by a tangent to the circle and a chord of the circle and has a vertex on the circle. Its measure is half the measure of the intercepted arc.

m<1 = (1/2)m(arc)BC = (1/2) * 100 deg = 50 deg

Answer: C. 50 deg