Q: Are central angles equal to the measure of their intercepted arcs?

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Yes. Two obtuse angles, of equal measure.Yes. Two obtuse angles, of equal measure.Yes. Two obtuse angles, of equal measure.Yes. Two obtuse angles, of equal measure.

Only when it is a regular polygon that all interior angles are of equal measure

corresponding angles are equal and alternate angles are equal

equal.

They have equal measure.

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Examples to show how to use the property that the measure of a central angle is equal to the measure of its intercepted arc to find the missing measures of arcs and angles in given figures.

In a circle, a central angle is formed by two radii. By definition, the measure of the intercepted arc is equal to the central angle.

All of the central angles in any polygon add up to 360 degrees.If the octogon is regular ... all of its central angles are equal ...then each of them is 45 degrees.

72 degrees 72 degrees

Yes. Two obtuse angles, of equal measure.Yes. Two obtuse angles, of equal measure.Yes. Two obtuse angles, of equal measure.Yes. Two obtuse angles, of equal measure.

It is true that the measure of a tangent-chord angle is half the measure of the intercepted arc inside the angle. When a tangent line intersects a chord of a circle, it creates an angle between the tangent line and the chord, known as the tangent-chord angle. If we draw a segment from the center of the circle to the midpoint of the chord, it will bisect the chord, and the tangent-chord angle will be formed by two smaller angles, one at each end of this segment. Now, the intercepted arc inside the tangent-chord angle is the arc that lies between the endpoints of the chord and is inside the angle. The measure of this arc is half the measure of the central angle that subtends the same arc, which is equal to the measure of the angle formed by the two smaller angles at the ends of the segment that bisects the chord. Therefore, we can conclude that the measure of a tangent-chord angle is half the measure of the intercepted arc inside the angle.

Only when it is a regular polygon that all interior angles are of equal measure

A square

corresponding angles are equal and alternate angles are equal

An isosceles triangle has two equal angles.

Congruent angles (or equivalent angles) have the same angle measure.

Not true. If the associated central angles are equal, the two chords would be equal.