Question

Take a look at the following figure if angle B measures 78°, and is the measure of BDC?

a. 204 degree

b. 156 degree

c. 39 degree

d. 78 degree

Answer 1

Option a. 204 degree

Explanation:

see the attached figure to better understand the problem

we know that

The semi-inscribed angle is half that of the arc it comprises.

so

∠B=(1/2)[arc BC]

substitute

78°=(1/2)[arc BC]

arc BC=156°

Remember that

arc BC+arc BCD=360°

arc BCD=360°-156°=204°