Circle Theorems
Rule

Circumscribed Angle Theorem

The measure of a circumscribed angle is equal to minus the measure of the central angle that intercepts the same arc.

Considering the above diagram, the following relation holds true.

Proof

By definition, a circumscribed angle is an angle whose sides are tangents to a circle. Since is a circumscribed angle, and are tangents to at points and respectively. By the Tangent to Circle Theorem, is perpendicular to and is perpendicular to

Notice that is a quadrilateral and two of its angles are right angles. Recall that the sum of all of the angles in a quadrilateral is Substituting the known angle measures and solving for will give the desired equation.
Solve for
This completes the proof.