8-2A Arcs and Central Angles

What is a central angle?

How are arcs defined?

What is a major arc?

What is a minor arc?

What is the measure of a semicircle?

Circles Graphs

Turn to page 564 in your book and look at the land areas of continents.

Central angles

Central angles are angles whose vertices are at the center of the circle.

Central angle

Arcs—parts of a circle

There are three kinds of arcs made by central angles:

Major arcs: greater than 180°

Named with 3 letters

Minor arcs: less than 180°

Named with 2 letters

Semi-circles: exactly 180°

Named with 3 letters

one-half of a circle

A

B

C

D

Major arc ADB

A BC

D

Minor arc AB

Measures in Degrees

• Complete circle measures 360°.

• The measure of any semicircle is 180°.

(½ of a circle)

360°

A

B

C180°

Measures

• Measure of a minor arc is equal to the measure of the central angle.

• Measure of the major arc is equal to 360° minus the measure of its minor arc.

W

X

Y

Z

80°

XY

Z

W

80°mXZY = 360°−mWX

XWmWXYm

80

Find each arc measure in ּסL

• mMN

• mMPN

• mPQN

P

M

N

Q

L 54°

54°

306°

180°

Arc-Additional TheoremThe measure of two

adjacent, nonoverlapping arcs is the sum of the measures of the two arcs.

That is if C is on arc AB, then mAB = mAC + mCB

A

B

C

Find each arc measure.• mRST

• mDE

• mHGF

R

S

T

D

E

H

G

F

40°

60°

153°

38°

320°

120°

191°

Definition

Congruent arcs are arcs in the same circle (or congruent circles) that have the same measure.

A

BX

Y

60° 60°

• What is a central angle?

Central angles are angles whose vertices are at the center of the circle.

How are arcs defined?

Arcs are defined as major arcs, minor arcs and semi circles.

• What is a major arc?

An arc that is greater than 180°• What is a minor arc?

An arc that is less than 180°• What is the measure of a semicircle?

Exactly 180°.