Circles, Central Angles, and Arcs

Multiple Choice

What are the measures of angle 3 and angle 4?

• $$m\angle3\ =\ 70\degree,\ m\angle4\ \ =\ 65\degree$$

• $$m\angle3\ =\ 65\degree,\ m\angle4\ =\ 70\degree$$

• $$m\angle3\ =110\degree,\ m\angle4\ =\ 105\degree$$

• $$m\angle3\ =\ 105\degree,\ m\angle4\ =110\degree$$

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

Solve for x. Just type in the numeric value.

Fill in the Blanks

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.

Fill in the Blanks

Just type in the numeric value.

Multiple Choice

• $$m\angle PQR=68\degree$$

• $$m\angle PQR=34\degree$$

• $$m\angle PQR=292\degree$$

• $$m\angle PQR=112\degree$$

Exterior Angle

Fill in the Blanks

Solve for x. Just type in the numeric value.

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?

• $$m\angle DBC=65\degree$$

• $$m\angle DBC=87.5\degree$$

• $$m\angle DBC=120\degree$$

• $$m\angle DBC=62.5\degree$$

Multiple Choice

Find the measure of  $$\angle KML$$ .

• $$m\angle KML=10\degree$$  

• $$m\angle KML=75\degree$$  

• $$m\angle KML=42.5\degree$$  

• $$m\angle KML=47.5\degree$$