Angles and Circles

7.2 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.

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.

Fill in the Blank

Just type in the numeric value.

Exterior Angle

• An exterior angle is one whose vertex is outside the circle.

• The measure of the exterior angle is equal to half the difference of its corresponding arcs.

•  $\frac{1}{2}$  (Big Arc - Little Arc)

• OR (Big Arc - Little Arc)/2

Fill in the Blank

Solve for x. Just type in the numeric value.

Multiple Choice

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

• 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

Fill in the Blank

Find the measure of minor arc SN (where the question mark is). Type in the numeric value.

Fill in the Blank

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