In the diagram, point o is the center of the circle and madb = 43°. if maob = mboc, what is mbdc?

a) 45°
b) 43°
c) 41°
d) 37°
e) 33°

The answer is B) 43°
Angle ADB is an inscribed angle which means arc AB has an angle twice that of angle ADB. The angle of the arc would be the same as that of the central angle AOB. So, mAOB = 86°. And since, mAOB = mBOC, then mBOC = 86° and arc BC has a measure of 86° as well. Angle BDC intercepts the arc BC which means half of the angle of arc BC is mBDC. So, mBDC = 43°.