10-2 Measuring Angles and Arcs day 2
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10-2 Measuring Angles and Arcs day 2
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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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
p. 708
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Find each arc measure.
• mRST
• mDE
• mHGF
R
S
T
D
E
H
G
F
40°
60°
153°
38°
320°
120°
191°
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.
Substitution= 58 + 32
Answer:
Arc Addition Postulate
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Arc Addition Postulate
Substitution= 90 + 58
= mIMJ + mJMK
= 148
Answer:
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A. 180
B. 90
C. 52
D. 38
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A. 52
B. 90
C. 142
D. 180
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Arc Lengths
Arc lengths are the pieces of the circumference cut by central angles.
Arc lengths are measured in units of measure like inches and centimeters.
Can arc length be measured with a ruler?
Arc length
A
B
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p. 709
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Formula for Arc Length
360
degreesarc2 rL
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is a central angle of ּסK
Find the arc length (L) of JL to the nearest tenth.
C = 2 π r (circumference)
The arc covers 125° out of a total of 360° or
JKL
JK
L
125° 12 cm
360
125
2.26360
125122 L
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If the circumference of a circle is 21π, what is the length of a 30° arc?
B
A
C
30°
360
3021 L
5.54
7
12
21
12
121L
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Arc Length Equation
Substitution
Answer:
Use a calculator.cm
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Arc Length Equation
Substitution
Use a calculator.
Answer:
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Arc Length Equation
Substitution
Use a calculator.
Answer:
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A. 3.56 cm
B. 3.77 cm
C. 3.98 cm
D. 4.21 cm
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A. 36.56 cm
B. 37.79 cm
C. 38.61 cm
D. 40.21 cm
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A. 32.99 cm
B. 33.59 cm
C. 33.89 cm
D. 34.61 cm
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• What is an arc length?
Arc lengths are the pieces of the circumference cut by central angles.
• How do you find arc length?
360
degreesarc2L r
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