Inscribed Quadrilaterals

Front

What is an inscribed quadrilateral?

Back

A quadrilateral is inscribed in a circle if all its vertices lie on the circle.

Front

What is the relationship between an inscribed angle and its intercepted arc?

Back

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

Front

If an inscribed angle intercepts an arc of 120°, what is the measure of the inscribed angle?

Back

60°

Front

What is the sum of the opposite angles in an inscribed quadrilateral?

Back

The sum of the opposite angles in an inscribed quadrilateral is 180°.

Front

If angle A and angle C are opposite angles in an inscribed quadrilateral, and m∠A = 72°, what is m∠C?

Back

m∠C = 180° - 72° = 108°.

Front

How do you find the measure of an angle formed by two chords that intersect inside a circle?

Back

The measure of the angle is equal to half the sum of the measures of the arcs intercepted by the angle.

Front

If two inscribed angles intercept the same arc, what can be said about their measures?

Back

The inscribed angles are congruent.

Front

What is the formula for finding the measure of an angle formed by two secants that intersect outside a circle?

Back

The measure of the angle is equal to half the difference of the measures of the intercepted arcs.

Front

If angle B is inscribed in a circle and intercepts an arc measuring 80°, what is m∠B?

Back

m∠B = 40°.

Front

What is the relationship between the angles of an inscribed quadrilateral?

Back

The opposite angles of an inscribed quadrilateral are supplementary.