Exploring Inscribed Angles

What defines an inscribed angle in a circle?

• An angle that intersects the circle at two points

• An angle with its vertex on the circle

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

• An angle inside the circle but not touching it

How is the measure of an inscribed angle related to its intercepted arc?

• It is double the measure of the arc

• There is no relationship

• It is equal to the measure of the arc

• It is half the measure of the arc

What is the relationship between an angle formed by a tangent and a chord?

• It is double the measure of the intercepted arc

• It is unrelated to the intercepted arc

• It is half the measure of the intercepted arc

• It is equal to the measure of the intercepted arc

If the measure of angle ACB is 72 degrees, what is the measure of arc AB?

• 36 degrees

• 72 degrees

• 144 degrees

• 288 degrees

How do you find the measure of an arc if you know the measure of the inscribed angle?

• Multiply the angle measure by 2

• Subtract the angle measure from 360

• Divide the angle measure by 2

• Add 180 to the angle measure

If arc AB is represented as 5x - 22, and angle ACB as 2x - 7, what is the value of x?

• 5

• 8

• 15

• 22

For an angle formed by a tangent and a chord, if angle ACB is 72 degrees, what is the measure of arc AC?

• 144 degrees

• 36 degrees

• 288 degrees

• 72 degrees

If arc ADC is 298 degrees, what is the measure of angle ACB?

• 31 degrees

• 149 degrees

• 62 degrees

• 298 degrees

To solve for an angle given the arc's measure, you should:

• Subtract the arc's measure from 360

• Divide the arc's measure by 2

• Multiply the arc's measure by 2

• Add 180 to the arc's measure

What is the measure of the remaining arc if arc ADC is 298 degrees?

• 62 degrees

• 72 degrees

• 298 degrees

• 360 degrees