Exploring Central and Inscribed Angles

This video tutorial covers central and inscribed angles in a circle. It begins by explaining arc measure and the concept that a full circle is 360 degrees. The video then distinguishes between central angles, where the angle is at the circle's center, and inscribed angles, where the angle is on the circle's surface. The relationship between the angle and arc measure is discussed, with examples provided to illustrate these concepts. The tutorial also includes solving equations involving these angles, with both simple and advanced problems.

What is the total degree measure of a circle?

• 270 degrees

• 360 degrees

• 180 degrees

• 90 degrees

How is a central angle defined in a circle?

• An angle that intersects the circle at one point

• An angle with its vertex at the center of the circle

• An angle with its vertex on the circle

• An angle with its vertex outside the circle

What is the relationship between a central angle and its intercepted arc?

• There is no relationship

• The angle's measure is equal to the measure of the arc

• The angle's measure is twice the measure of the arc

• The angle's measure is half the measure of the arc

How does an inscribed angle's measure relate to its intercepted arc?

• It is twice the measure of the arc

• It is one-fourth the measure of the arc

• It is equal to the measure of the arc

• It is half the measure of the arc

What is the measure of an arc intercepted by an inscribed angle of 30 degrees?

• 15 degrees

• 30 degrees

• 120 degrees

• 60 degrees

What is the correct formula to find the measure of an inscribed angle when the arc measure is known?

• Angle measure = Arc measure / 2

• Arc measure = Angle measure / 2

• Arc measure = 2 * Angle measure

• Angle measure = 2 * Arc measure

If the measure of a central angle is 82 degrees, what is the measure of its intercepted arc?

• None of the above

• 164 degrees

• 82 degrees

• 41 degrees

If an inscribed angle measures 65 degrees, what is the measure of its intercepted arc?

• 65 degrees

• 260 degrees

• 130 degrees

• 32.5 degrees

Given a central angle of 3x + 20 degrees, and an arc measure of 4x - 10 degrees, what is the value of x?

• 30

• 40

• 10

• 20

For an inscribed angle with a measure of 2x + 5 degrees and an arc measure of 3x + 30 degrees, what is x?

• 5

• 10

• 15

• 20