Exploring Inscribed and Central Angles

This video tutorial covers central and inscribed angles within a circle, explaining their properties and how to calculate arc measures. It includes a review of central angles, the relationship between angles and arcs, and the use of percentages to determine arc measures. The video also discusses key theorems related to inscribed angles, such as the measure of an inscribed angle being half of its intercepted arc, and provides practice problems to reinforce these concepts.

What is the measure of an arc intercepted by a central angle of 85 degrees?

• 42.5 degrees

• 85 degrees

• 170 degrees

• 360 degrees

If the central angle corresponding to arc CD is 58 degrees, what is the measure of arc CD?

• 180 degrees

• 58 degrees

• 116 degrees

• 29 degrees

How do you calculate the measure of an arc representing 14% of a circle?

• 0.14 times 360

• 14 plus 360

• Divide 360 by 14

• Multiply 14 by 360

What is the measure of an inscribed angle if its intercepted arc is 100 degrees?

• 100 degrees

• 200 degrees

• 25 degrees

• 50 degrees

If an inscribed angle measures 76 degrees, what is the measure of its intercepted arc?

• 304 degrees

• 76 degrees

• 152 degrees

• 38 degrees

What is the relationship between the opposite angles of a quadrilateral inscribed in a circle?

• They are equal.

• They are supplementary.

• They are both acute angles.

• They are complementary.

An angle inscribed in a semicircle is always what type of angle?

• Obtuse

• Right

• Straight

• Acute

What is the measure of an angle formed by a chord and a tangent if the intercepted arc is 200 degrees?

• 400 degrees

• 100 degrees

• 200 degrees

• 50 degrees

If angle ACD is 62 degrees and arc CD is 58 degrees, what is the measure of arc AD?

• 124 degrees

• 58 degrees

• 62 degrees

• 116 degrees

Given that arc AB is 110 degrees and arc BC is 48 degrees, what is the measure of arc CD?

• 110 degrees

• 48 degrees

• 202 degrees

• 68 degrees