Inscribed Angles and Their Measures

An angle is inscribed if and only if its vertex lies on the circle and its sides contain chords of the circle.

Inscribed Angle Theorem: If an angle is inscribed in a circle, then its measure equals one-half the measure of its intercepted arc (or the measure of the intercepted arc is twice the measure of the inscribed angle).

Arc – Intercept Corollary: If two inscribed angles of a circle (or congruent circles) intercept congruent arcs or the same arc, then the angles are congruent.

Right Angle Corollary: If an inscribed angle of a circle intercepts a semicircle, then the angle is a right angle.

Cyclic Quadrilateral Theorem: If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

Read the explanation below to learn more about inscribed angles.

Inscribed Angles and Their Measures

Practice: Identify and use properties of inscribed angles in the following exercises.

Inscribed Angles and Their Measures 1

Inscribed Angles and Their Measures 2

Inscribed Angles and Their Measures 3

Inscribed Angles and Their Measures 4

Inscribed Angles and Their Measures 5

Inscribed Angles and Their Measures 6