Central, Inscribed, and Circumscribed Angles

Identify the angle highlighted in blue.

• Center of the circle

• minor arc

• Central angle

• Inscribed angle

What formula would you use to find m<A?

• angle = 1/2 (arc + arc)

• angle = 1/2 (arc - arc)

• angle = 1/2(arc)

• circumscribed angle = 180 - central angle

Answer explanation

<A is an inscribed angle.
angle = 1/2(arc)

What formula would you use to find m<1?

• angle = 1/2 (arc + arc)

• angle = 1/2 (arc - arc)

• angle = 1/2(arc)

• circumscribed angle = 180 - central angle

Answer explanation

<1 is created from the tangent line, m, and chord AB. 
angle = 1/2(intercepted arc)

What formula would you use to find m<x?

• angle = 1/2 (arc + arc)

• angle = 1/2 (arc - arc)

• angle = 1/2(arc)

• circumscribed angle = 180 - central angle

Answer explanation

<x is created from the secants that cross INSIDE the circle.

angle = 1/2 (arc + arc)

What formula would you use to find m<x?

• angle = 1/2 (arc + arc)

• angle = 1/2 (arc - arc)

• angle = 1/2(arc)

• circumscribed angle = 180 - central angle

Answer explanation

<x is created from the secants that cross OUTSIDE the circle.

angle = 1/2 (larger arc - smaller arc)

The sides of circumscribed angles are _________ to the circle.

<B is the circumscribed angle.

• tangent

• secant

• parallel

• perpendicular

Answer explanation

tangent = touches the circle at one point

What formula would you use to find m<x?

• angle = 1/2 (arc + arc)

• angle = 1/2 (arc - arc)

• angle = 1/2(arc)

• circumscribed angle = 180 - central angle

Answer explanation

<x is created from the two tangent lines. It is a circumscribed angle.

circumscribed angle = 180 - central angle

What formula would you use to find y?

• angle = 1/2 (arc + arc)

• 180 = opposite angle + opposite angle

• angle = 1/2(arc)

• circumscribed angle = 180 - central angle

Answer explanation

180 = opposite angle + opposite angle

Identify the angle highlighted in pink

• center of the circle

• minor arc

• central angle

• inscribed angle

What type of angles are the two highlighted angles?

• Central angles

• Supplementary Angles

• Vertical Angles

• Inscribed Angles