Central and Inscribed Angles

Front

What is a central angle?

Back

A central angle is an angle whose vertex is at the center of a circle and whose sides (rays) extend to the circumference.

Tags

CCSS.HSG.C.A.2

Front

What is an inscribed angle?

Back

An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. The vertex of the angle is on the circle.

Tags

CCSS.4.MD.C.5B

CCSS.HSG.CO.A.1

Front

What is the relationship between a central angle and an inscribed angle that subtend the same arc?

Back

The measure of a central angle is twice the measure of the inscribed angle that subtends the same arc.

Tags

CCSS.HSG.C.A.2

Front

How do you calculate the measure of an inscribed angle?

Back

The measure of an inscribed angle is half the measure of the intercepted arc.

Tags

CCSS.HSG.C.A.2

Front

If the measure of arc AB is 80°, what is the measure of the inscribed angle ACB?

Back

The measure of angle ACB is 40°.

Tags

CCSS.HSG.C.A.2

Front

What is the formula to find the measure of an inscribed angle?

Back

The formula is: Measure of inscribed angle = 1/2 * Measure of intercepted arc.

Tags

CCSS.HSG.C.A.2

Front

What is the measure of a central angle if the inscribed angle is 30°?

Back

The measure of the central angle is 60°.

Tags

CCSS.HSG.C.A.2

Front

If angle K measures 55°, what is the measure of arc JK?

Back

The measure of arc JK is 110°.

Front

What is the sum of the measures of angles in a triangle?

Back

The sum of the measures of angles in a triangle is always 180°.

Tags

CCSS.8.G.A.5

Front

If angle ABC measures 50°, what is the measure of the arc subtended by angle ABC?

Back

The measure of the arc subtended by angle ABC is 100°.