4.1b Lesson: Inscribed Angles in Circles

4.1b Lesson: Inscribed Angles in Circles

SOL G.11.a

I can describe arc measures associated with inscribed angles.

Open Ended

How do you know the given image is a circle?

How can you verify or prove that it is a circle?

Show your work!

Multiple Choice

Find the measure of Arc TW.

• 319º

• 41º

• 360º

• 82º

Inscribed Angles

Inscribed Angles are angles with their vertex ON the circle.

They look like this ------------------>

Here are some NON-examples. These are NOT inscribed angles.

Inscribed Angles vs. Central Angles

Multiple Choice

What is the measure of arc PR ?

• 360º

• 45º

• 90º

• 180º

Inscribed Angles vs. Central Angles

Open Ended

In general, what can you tell about the measure of

 $\angle PQR$  compared to 

$\ange$

 ?

Take a look at this animation similar to our Circle O

Inscribed Angles have a measure that is exactly HALF of the measure of their intercepted arc.

Multiple Choice

What is the measure of

 $\angle EDF$  ?
(click image to enlarge)

• 120º

• 60º

• 180º

• 360º

Multiple Choice

What is the measure of

 $\angle XWE$  ?
(click image to enlarge)

• 180º

• 112º

• 56º

• 360º

Multiple Choice

Find the measure of the

 $arc\ \overline{DC}$  .
(click image to enlarge)

• 124º

• 62º

• 31º

• 360º

Multiple Choice

Find the measure of the

 $arc\ \overline{XW}$ .
(click image to enlarge)

• 56º

• 180º

• 360º

• 106º