Question

The Circumscribed Angle Theorem states that a circumscribed angle of a circle and its associated central angle are supplementary. Explain why this theorem is true. Refer to the visual model shown.

Answer 1

Explanation:

AC is the radius of the circle. BC has the same length as AC.

A 90 degree angle is formed at A, similarly ay B.

A quadrilateral is then formed.

The sum of angles in a quadrilateral is 360 degrees

We have:

A + B + C + D = 360

90 + 90 + C + D = 360

C + D = 360 - 180

C + D = 180

Hence the proof