A central angle is one angle v its vertex at the center of a circle, with its sides containing two radii of the circle.

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In the figure above, ∠ p Z Q , ∠ Q Z R , and ∠ R Z p are central angles.

sum of central Angles: The amount of the procedures of the main angles of a circle v no clues in common is 360 ° .

because that example, in the figure above,

m ∠ p Z R + m ∠ R Z Q + m ∠ Q Z ns = 360 ° .


Example:

uncover the value of x .

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The sum of the actions of the main angles the a circle through no inner points in usual is 360 ° .So,

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

Simplify.

140 ° + x = 360 °

Subtract 140 ° from every side.

x = 220 °


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