1. Central Angles and Arc Length
Lesson 10-2
Central Angles and Arc Length
Lesson 10-2

2. Central Angle Definition:
An angle whose vertex lies on the center of the circle.
Central Angle
(of a circle)
Central Angle
(of a circle)
NOT A Central Angle
(of a circle)
Lesson 10-2

3. Central Angle Theorem
The measure of a center angle is equal to the measure of the intercepted arc. Y Z O
110
Intercepted Arc
Center Angle
Example:
Give is the diameter, find the value of x and y and z in the figure.
Lesson 10-2

4. Example: Find the measure of each arc.
4x + 3x + (3x +10) + 2x + (2x-14) = 360°
14x – 4 = 360°
14x = 364°
x = 26°
4x = 4(26) = 104°
3x = 3(26) = 78°
3x +10 = 3(26) +10= 88°
2x = 2(26) = 52°
2x – 14 = 2(26) – 14 = 38°
Lesson 10-2

5. Arc Length Arc length is the distance around an arc. Formula:
The circumference multiplied by the ratio of the center angle and 360°.
Example:
Arc Length 2 cm 72 B C A
Lesson 10-2