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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.
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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
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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
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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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p. 707
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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
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Answer:
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Answer:
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Answer:
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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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p. 707
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mLPK = 0.21(360) Find 21% of 360.
= 75.6 Simplify.
Answer:
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Sum of arcs in a circle is 360.
SubstitutionSimplify.Simplify.
Answer:
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A. 124.3
B. 140.4
C. 155.6
D. 165.9
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Find each arc measure in ּסL
• mMN
• mMPN
• mPQN
P
M
N
Q
L 54°
54°
306°
180°
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