Angles of Circles

Angles of 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

• Interior Angle

• Exterior 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.

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 Blanks

Fill in the Blanks

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.

Fill in the Blanks

Multiple Choice

• $$m\angle PQR=68\degree$$

• $$m\angle PQR=34\degree$$

• $$m\angle PQR=292\degree$$

• $$m\angle PQR=112\degree$$

Exterior Angle

Fill in the Blanks

Multiple Choice

Solve for x.

• 34

• 17

• 23

• 27

Multiple Choice

Find the measure of the central angle (pink angle, one question mark).

• 104 degrees

• 52 degrees

• 128 degrees

• 76 degrees

Multiple Choice

Find the measure of the exterior angle (blue angle, two question marks).

• 104 degrees

• 52 degrees

• 128 degrees

• 76 degrees

Interior Angle

• An interior angle has a vertex inside the circle and is formed by two intersecting chords/secants.

• The measure of an interior angle is half the sum of its corresponding arcs.

• (arc1 + arc2)/2

Multiple Choice

What is the measure of the angle DBC?

• $$m\angle DBC=65\degree$$

• $$m\angle DBC=87.5\degree$$

• $$m\angle DBC=120\degree$$

• $$m\angle DBC=62.5\degree$$

Fill in the Blanks

Multiple Choice

Find the measure of  $$\angle KML$$ .

• $$m\angle KML=10\degree$$  

• $$m\angle KML=75\degree$$  

• $$m\angle KML=42.5\degree$$  

• $$m\angle KML=47.5\degree$$  

Fill in the Blanks

Inscribed Quadrilateral: opposite angles =180

When a quadrilateral is inscribed in a circle, the opposite angles always add to 180.

Multiple Select

Select all equations that can be used to solve for x and y in the following inscribed quadrilateral.

• x+55=180

• y+85=180

• x+85=180

• y+55=180

Practice Time

Multiple Choice

Find the m∠2.

• 80⁰
• 45⁰
• 125⁰
• 40⁰

Multiple Choice

Find the m∠ABE.

• 129⁰
• 51⁰
• 100⁰
• 65⁰

Multiple Choice

Find m∠UST.

• 119°
• 163°
• 44°
• 61°

Multiple Choice

Find the measure of minor arc AV.

• 55°
• 115°
• 85°
• 95°

Multiple Choice

Find the measure of minor arc  AC.

• 76°
• 135.5°
• 70.5°
• 65°

Multiple Choice

Find the m∠MNQ.

• 89⁰
• 45⁰
• 158⁰
• 22⁰

Multiple Choice

Find the m∠1.

• 130⁰
• 65⁰
• 44⁰
• 86⁰

Multiple Choice

What is the measure of major arc AYB?

• 50 degrees

• 100 degrees

• 180 degrees

• 260 degrees

Multiple Choice

What is x?

• 15

• 23

• 2

• 92

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

• 23.5

• 180

• 86˚

• 360