6.2 Inscribed Angles and Inscribed Quadrilaterals

Front

What is an inscribed angle?

Back

An inscribed angle is formed by two chords in a circle which have a common endpoint. The vertex of the angle is on the circle, and the sides of the angle are the chords.

Front

What is the relationship between an inscribed angle and the arc it intercepts?

Back

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

Front

What is the measure of an angle inscribed in a semicircle?

Back

An angle inscribed in a semicircle is a right angle (90°).

Front

What are the properties of angles in an inscribed quadrilateral?

Back

In an inscribed quadrilateral, opposite angles are supplementary, meaning their measures add up to 180°.

Front

If angle A and angle C are inscribed in a circle, what can be said about their measures if they intercept the same arc?

Back

If angle A and angle C intercept the same arc, then m∠A = m∠C.

Front

How do you find the measure of an inscribed angle if you know the measure of the intercepted arc?

Back

To find the measure of an inscribed angle, divide the measure of the intercepted arc by 2.

Front

What is the formula for finding the measure of an angle formed by two intersecting chords?

Back

The measure of the angle formed by two intersecting chords is equal to half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

Front

What is the relationship between the angles formed by two secants that intersect outside a circle?

Back

The measure of the angle formed by two secants that intersect outside a circle is equal to half the difference of the measures of the intercepted arcs.

Front

If angle W measures 129°, what is the measure of the arc it intercepts?

Back

The measure of the intercepted arc is 2 * 129° = 258°.

Front

What is the measure of angle A if it intercepts an arc measuring 112°?

Back

The measure of angle A is 112° / 2 = 56°.