Circles Angles

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.

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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.

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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

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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 Blanks

Fill in the Blanks