Question

Which angles intercept a 20 degree arc in a circle? Select all that apply.

a. A central angle of 10 degrees
b. A central angle of 20 degrees
c. A central angle of 40 degrees
d. An inscribed angle of 10 degrees
e. An inscribed angle of 20 degrees
f. An inscribed angle of 40 degrees

Answer 1

B and D

Explanation:

A 20 degree intercepted arc will correspond with two angles: the inscribed angle and the central angle.

The central angle always has the same degree measure as the intercepted arc, so we want a central angle with degree 20. So, that's B.

The inscribed angle is the angle whose vertex is on the circle, not the center. This angle always has half the measure of the intercepted arc, so we want an angle with degree 20/2 = 10. So, that's D.

Thus, the answers are B and D.

Hope this helps!