Exploring Central and Inscribed Angles

What defines a central angle in a circle?

• An angle that is twice the measure of its intercepted arc

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

• An angle with its vertex on the circle's circumference

• An angle that is equal to half the measure of its intercepted arc

If a central angle measures 30 degrees, what is the measure of its intercepted arc?

• 45 degrees

• 60 degrees

• 30 degrees

• 15 degrees

How to find the measure of a central angle given the measure of its intercepted arc?

• Multiply the arc's measure by 2

• Divide the arc's measure by 2

• The measure is the same as the arc's

• Subtract the arc's measure from 180 degrees

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

• There is no specific relationship

• The angle is twice the arc's measure

• The angle and arc have equal measures

• The angle is half the arc's measure

What is true about an inscribed angle in a circle?

• Its vertex is at the center of the circle

• It is equal to the measure of its intercepted arc

• Its vertex is on the circle's circumference

• It is twice the measure of its intercepted arc

If an arc measures 80 degrees, what is the measure of an inscribed angle intercepting this arc?

• 80 degrees

• 40 degrees

• 20 degrees

• 160 degrees

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

• 200 degrees

• 100 degrees

• 50 degrees

• 25 degrees

How does the measure of an inscribed angle compare to its intercepted arc?

• It is double

• It is half

• It is the same

• It is one-fourth

In a circle, if arc BC measures 38 degrees, what is the measure of a central angle intercepting arc BC?

• 57 degrees

• 19 degrees

• 38 degrees

• 76 degrees

Given arc RS measures 120 degrees, what is the measure of an inscribed angle intercepting arc RS?

• 240 degrees

• 120 degrees

• 60 degrees

• 30 degrees