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

Take a look at the Central Angle  $\angle POR$  to the right. It has the intercepted arc PR. 

What do you know about the measure of arc PR?

Multiple Choice

What is the measure of arc PR ?

• 360º

• 45º

• 90º

• 180º

Inscribed Angles vs. Central Angles

 $\angle PQR$  shares the same intercepted arc PR. 

Do the measure of the central angle and inscribed angle appear equal?

Open Ended

In general, what can you tell about the measure of

$$\angle PQR$$  compared to  $$\angle PQR$$

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.

 $arc\ \overline{PR}\ =\ 90\degree$  
 $\angle PQR=45\degree$  

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

Poll

Choose the option that best describes you.

• I understand inscribed angles and arcs completely so far. I could answer more difficult questions on my own.

• I think I understand inscribed angles and arcs, but I need more practice right now.

• I need to be retaught the entire lesson.

Find the 4.1b Practice: Inscribed Angles in Circles (SOL G.11.b) ✏️