Circle Properties and Angles
CONCEPTS
Properties of Central Angle
• Central angle, θ, is the angle of a sector. It has 2 lines extending from the center to a point on the circle
• Central angle (θ) = 360° * area of sector / area of circle
Central angle (θ) = 360° * circumference of sector / circumference of circle
Arc length
• Arc length is the length of the circle encompassed by the sector
• Arc length (or sector circumference) = 2πr * θ / 360°
Sector area
• Sector area = πr² * θ / 360°
PRACTICE PROBLEMS
Question 1 A sector of a circle has an area equal to 5/12 of the area of the circle. What is the measure of the sectors central angle?
-- Answer -- 150°
5/12 * 360° = 150°
Question 2 A fan has 5 identical blades evenly spaced around the center of the fan. What’s the measure of the angle that would move Blade M to the Blade N position (see figure below)?
-- Answer -- 72°
360° / 5 = 72°
ACT PRACTICE PROBLEMS