10.4 Inscribed Angles & Polygons

Front

What is an inscribed angle?

Back

An inscribed angle is an angle 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

If the measure of arc AB is 68°, what is the measure of the inscribed angle that intercepts arc AB?

Back

34°

Front

What is the formula for finding the measure of an arc in a circle?

Back

The measure of an arc can be found using the formula: Arc Measure = (Central Angle) x (180°/π) if the angle is in radians.

Front

How do you find 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

What is the measure of angle A if it intercepts an arc measuring 190°?

Back

Angle A measures 95°.

Front

What is the relationship between the angles formed by two intersecting chords?

Back

The measure of each 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

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

Back

The two angles are equal in measure.

Front

What is the measure of angle B if it intercepts an arc measuring 146°?

Back

Angle B measures 73°.

Front

How do you find the value of x in an inscribed angle problem?

Back

Set up an equation based on the relationship between the inscribed angle and the intercepted arc, then solve for x.