1. Central Angles & Their Measures
Sector
Arc
Central Angle

2. Intercepted Arc of a Central Angle = Measure of Angle ·Radius
Arc = rØ˚ where r = radius & Ø˚= central angle
Measure of Central Angle Ø˚ = •360˚
(and then multiply by IF they want answer in radians
OR )
Area of Sector = or

3. Ex: Given the measure of a central angle is π/6, find the measure
of the intercepted arc (in terms of π) in a circle of radius 10 cm.
Ex: This time, the central angle is 10˚ and the diameter is 60 in.
10˚•30 =
300
which in terms of π is:
300• π or
1 180
5 π in. 3

4. Ex: Given the measure of an arc is 87 cm, find the degree
measure (to nearest tenth) of the central angle in a circle of
radius 16 cm.
Arc measure 360
Circumference
Central Angle=
360
2•π•16
311.5˚

5. Ex: Find the area of the sector (to nearest tenth) if the central
angle is π⁄6 and radius is 14 cm.
Area of sector= Central Angle  πr2 which is 2π
51.3 cm2