Description

Here is a short description of the angle relationships shown in Figure 120:In a circle with center O, if angle AOC is 120°, then:

• Angle APC is 60°, since the angle subtended by an arc at the center is double the angle subtended by it on any remaining part of the circle.
• Angle ABC is 120°, since opposite angles in a cyclic quadrilateral are supplementary to 180°.
• Angle BDC is 100°, since angle AOB is 40° and angle BDC is the supplementary angle to AOB.

So in summary, if angle AOC is 120°, then angle ABC is also 120° and angle BDC is 100°. The figure illustrates these angle relationships within the circle