10-2 Measuring Angles and Arcs

You measured angles and identified congruent angles.

• Identify central angles, major arcs, minor arcs, and semicircles, and find their measures.

• Find arc lengths.

Central anglesCentral angles are

angles whose vertices are at the center of the circle.

Central angle

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Find Measures of Central Angles

Find the value of x.

Substitution

Simplify.

Add 2 to each side.

Divide each side by 26.

The sum of the measures of

Answer: x = 7

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°

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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

Answer:

Answer:

Answer:

Definition

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

A

BX

Y

60° 60°

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mLPK = 0.21(360) Find 21% of 360.

= 75.6 Simplify.

Answer:

Sum of arcs in a circle is 360.

SubstitutionSimplify.Simplify.

Answer:

A. 124.3

B. 140.4

C. 155.6

D. 165.9

Find each arc measure in ּסL

• mMN

• mMPN

• mPQN

P

M

N

Q

L 54°

54°

306°

180°