Page 158 - Math Course 3 (Book 2)

Circles: Angles and Arcs

Arc Length
Your Turn!

Example Circle Graphs

SPEED LIMITS
In ⊙B, AC = 9 and m∠ABD = 40. This graph shows the percent of U.S. states that
have each speed limit on their interstate highways.
Find the length of AD. Find the measurement of the central angles
representing each category. List them from
least to greatest.
A B

C
D

In ⊙B, AC = 9 so C = π(9) or 9π and mAD = m∠ABD
or 40. Write a proportion to compare each part to its
whole.

degree A. 3.6°, 72°, 64.8°, 39.6°
measure B. 3.6°, 39.6°, 64.8°, 72°
of arc → 40 ℓ ← arc length C. 7.2°, 144°, 129.6°, 79.2°
degree → 360 = 9π ← circumference D. 7.2°, 79.2°, 129.6°, 144°
measure
of whole
circle Answer

Now solve the proportion for ℓ. This graph shows the percent of U.S. states that
have each speed limit on their interstate highways.
40 ℓ Is the arc for the wedge for 65 mph congruent to
360 = 9π the combined arcs for the wedges for 55 mph and
70 mph?
40
360 (9π) = ℓ Multiply each side by 9 π. A. yes
B. no
π = ℓ Simplify. C. cannot be determined

Answer
Answer The length of AD is π units or
about 3.14 units.

Arc Length

In ⊙A, AY = 21 and m∠XAY = 45. Find the length of WX to the nearest hundredth.

A. 7.88
B. 15.75 W X
C. 49.48
D. 24.74
Z A Y
Answer

150