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Theorem 9

The measure of an inscribed angle is half the measure of its intercepted arc.

Corollary 3

The opposite angles of a quadrilateral inscribed in a circle are supplementary.

Corollary 1

Two inscribed angles that intercept the same arc are congruent

Corollary 2

Example 1

An angle inscribed in a semicircle is a right angle.

What is an inscribed angle?

An angle is inscribed in a circle if the vertex of the angle is on the circle and the sides of the angle are chords of the circle.

Find the measure of the numbered angle.

An intercepted arc is an arc of a circle having endpoints on the side of an inscribed angle, and its other points in the interior of the angle.

Example 2

Theorem 10

The measure of an angle formed by tangent and a chord is half the measure of the intercepted arc.

Find the value of each variable.

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