Exploring Central and Inscribed Angles of a Circle

This video tutorial covers central and inscribed angles in circles, explaining their definitions and properties. It discusses arcs, including minor, major, and semicircles, and introduces the arc addition postulate. The tutorial provides examples and problem-solving techniques for calculating angle measures and arc lengths, emphasizing the relationship between inscribed angles and intercepted arcs.

What is a central angle in a circle?

• An angle formed by two tangents to the circle

• 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

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CCSS.HSG.C.A.2

How is the measure of a minor arc determined?

• It is 360 degrees minus the measure of its central angle

• It is half the measure of its central angle

• It is equal to the measure of its central angle

• It is double the measure of its central angle

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CCSS.HSG.C.B.5

What is the measure of a semicircle?

• 180 degrees

• 270 degrees

• 90 degrees

• 360 degrees

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CCSS.4.MD.C.5B

CCSS.HSG.CO.A.1

According to the arc addition postulate, what is true about adjacent arcs?

• Their measures add up to the measure of the entire circle

• Their measures subtract to give the central angle

• Their measures add up to 180 degrees

• Their measures are equal

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CCSS.HSG.C.B.5

If a central angle measures 33 degrees, what is the measure of its corresponding arc?

• 132 degrees

• 99 degrees

• 66 degrees

• 33 degrees

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CCSS.HSG.C.B.5

What is the measure of an inscribed angle that intercepts a semicircle?

• 90 degrees

• 135 degrees

• 45 degrees

• 180 degrees

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CCSS.HSG.C.A.2

If an inscribed angle measures 54 degrees, what is the measure of its intercepted arc?

• 108 degrees

• 54 degrees

• 216 degrees

• 27 degrees

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CCSS.HSG.C.A.2

How is the measure of arc AE determined if angle EDF is 15 degrees and arc AF is 94 degrees?

• 30 degrees

• 60 degrees

• 94 degrees

• 124 degrees

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CCSS.HSG.C.B.5

What is the measure of angle ABE if arc AE is 124 degrees?

• 62 degrees

• 124 degrees

• 248 degrees

• 31 degrees

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CCSS.HSG.C.A.2

If an inscribed angle measures 15 degrees, what is the measure of its intercepted arc?

• 15 degrees

• 30 degrees

• 60 degrees

• 45 degrees

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CCSS.HSG.C.A.2