Page 157 - Math Course 3 (Book 2)

Circles: Angles and Arcs

MO. 11 - L2b
Let’s Begin

Arc Length of a Circle

Circle Graphs

THEOREM 11.1 Example

In the same or in congruent circles, two arcs are
congruent if and only if their corresponding central BICYCLES
angles are congruent. This graph shows the percent of each type of
bicycle sold in the United States in 2001. Find the
measurement of the central angle representing
POSTULATE 11.1 each category. List them from least to greatest.

Bicycle Bought Last Year
Arc Addition Postulate (by type)

The measure of an arc formed by two adjacent arc
is the sum of the measure of the two arcs.
Mountain
Example: In ⊙S, mPQ + mQR = mPQR. Youth 37%
26%
P
Hybrid 9% Other 7% Comfort

21%
S
The sum of the percents is 100% and represents
the whole. Use the percents to determine what
R Q part of the whole circle (360°) each central angle
contains.

7%(360°) = 25.2° 26%(360°) = 93.6°
Key Concept 9%(360°) = 32.4° 37%(360°) = 133.2°
21%(360°) = 75.6°

Arc Length Answer 25.2°, 32.4°, 75.6°, 93.6°, 133.2°

degree
measure This graph shows the percent of each type of
of arc → A = ℓ ← arc length bicycle sold in the United States in 2001. Is the arc
360 2πr ← circumference for the wedge named Youth congruent to the arc for
degree → the combined wedges named Other and Comfort?
measure
of whole The arc for the wedge named Youth represents
circle
26% or 93.6% of the circle. The combined wedges
A named Other and Comfort represent 7% + 21% =
This can also be expressed as • C = ℓ. 28% or 25.2° + 75.6º = 100.8º. Since 93.6º ≠ 100.8º,
360 the arcs are not congruent.

Answer NO

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