Math Homework. Do It Faster, Learn It Better.
Central Angles
A central angle is an angle with its vertex at the center of a circle, with its sides containing two radii of the circle.
In the figure above, , and are central angles.
Sum of Central Angles: The sum of the measures of the central angles of a circle with no points in common is .
For example, in the figure above,
.
Example:
Find the value of .
The sum of the measures of the central angles of a circle with no interior points in common is . So,
Simplify.
Subtract from each side.