how to find the central angle

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, ∠ P Z Q , ∠ Q Z R , and ∠ R Z P 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 360 ° .

For example, in the figure above,

m ∠ P Z R + m ∠ R Z Q + m ∠ Q Z P = 360 ° .

Example:

Find the value of x .

The sum of the measures of the central angles of a circle with no interior points in common is 360 ° .So,

m ∠ M O N + m ∠ N O P + m ∠ P O M = 360 ° 50 ° + 90 ° + x = 360 °

Simplify.

140 ° + x = 360 °

Subtract 140 ° from each side.

x = 220 °

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