12-3 Inscribed angles

Inscribed angles

By Deb Scott

Vocab:

• Inscribed angle: When two lines connect one point on the surface of a circle with two other points on that circle

• Intercepted arc: an arc formed when one or two different chords or line segments cut across a circle

The Inscribed angle Theorem:

The measure of the inscribed angle is HALF the measure of the intercepted arc

Inscribed angles:

The measure of the inscribed angle is half the angle of the central angle (remember that central angles and intercepted arcs have the same measure).

Multiple Choice

What is the measure of the INTERCEPTED ARC?

• 72°

• 36°

• 30°

• 180°

Multiple Choice

What is the measure of the INSCRIBED ANGLE?

• 62°

• 124°

• 31°

• 180°

Multiple Choice

What is the measure of the INSCRIBED ANGLE?

• 324°

• 162°

• 81°

• 51°

Multiple Choice

What is the measure of the INSCRIBED ANGLE?

• 30°

• 50°

• 100°

• 60°

Multiple Choice

What is the value of x?

• 5

• -5

• -15

• -20

Multiple Choice

What is the value of x?

• 23

• 95

• 190

• 120

​What is the value of a? How do you know.

​

What is the value of b? How do you know.​

Draw

Find the measures of angles 1, 2, 3, and 4.

​Look at how point A shifts. Do you think the previous formula about angle measures still applies? Why

Multiple Choice

What is the value of x?

• 75

• 90

• 150

• 180

Multiple Choice

What is the value of w?

• 75

• 90

• 105

• 180

Multiple Choice

What is the value of y?

• 75

• 150

• 105

• 210

Once you've found x, what about y?

Think about what equation would be needed to find the value of y in this problem.

Let's do one more together.

Find the measure of angles L and N.

Multiple Choice

What is x?

• 15

• 23

• 2

• 92

Multiple Choice

Solve for x.

• 37.5

• 11

• 118

• 15