Angles and Arcs in Circles

Angles and Arcs in Circles

Goal: I can find missing measures of angles and arcs using circle theorems.

Today we are going to learn about the following:

• Central Angle

• Inscribed Angle

Central Angle

• A central angle of a circle has a vertex at the center and is formed by two radii.

• The measure of the central angle is the same as the measure of its corresponding arc of the circle.

Labelling

Use the angle measures to Label the diagram in a way that makes sense!

Drag labels to their correct position on the image

Multiple Choice

Find the measure of  $$\angle AOB$$   

• $$m\angle AOB=27\degree$$  

• $$m\angle AOB=333\degree$$  

• $$m\angle AOB=207\degree$$  

• $$m\angle AOB=13.5\degree$$  

Fill in the Blank

Solve for x. Just type in the numeric value.

Fill in the Blank

Find $$m\angle POQ$$

Just type in the numeric value.

Inscribed Angle

• An inscribed angle in a circle has a vertex on the circle and is formed by two chords.

• The measure of an inscribed angle is half the measure of its corresponding arc of the circle.

Labelling

Use the angle measures to Label the diagram in a way that makes sense!

Drag labels to their correct position on the image

Fill in the Blank

Just type in the numeric value.

Multiple Choice

• $$m\angle PQR=68\degree$$

• $$m\angle PQR=34\degree$$

• $$m\angle PQR=292\degree$$

• $$m\angle PQR=112\degree$$

Multiple Choice

• 17

• 34

• 68

• 146

Multiple Choice

• 70

• 140

• 35

• 88

Multiple Choice

• m∠K=100 & m∠M=100

• m∠K=50 & m∠M=50

• m∠K=100 & m∠M=50

• m∠K=50 & m∠M=100

Math Response

What is the measure of the missing angle in degrees?

Type answer here

Correct Answer: 51

Deg^°

Rad

Math Response

Find the measure of the missing angle in degrees.

Type answer here

Correct Answer: 41

Deg^°

Rad

Multiple Choice

Find a and b.

• a=74 degrees
  b=93 degrees
• a=93 degrees
  b=74 degrees
• a=87 degrees
  b=106 degrees
• a=106 degrees
  b=87 degrees

Multiple Choice

Find the arc measure for arc RQT

• 335˚

• 126˚

• 224˚

• 94˚

Multiple Choice

Given the following inscribed quadrilateral, what is the value of y?

• 10
• 20
• 30
• 40

Fill in the Blank

Find  $$m\angle EDF$$ . Type in the numeric value.

Math Response

What is the value of w?

Type answer here

Correct Answer: 104

Deg^°

Rad

Math Response

What is the value of y?

Type answer here

Correct Answer: 108

Deg^°

Rad

Multiple Choice

How many degrees are in a cirlce?

• 90
• 180
• 270
• 360