Sector central angle n=( 180L)/(πr) (degrees).

Where n is the degree of the central angle, l is the arc length and r is the radius.

L (arc length) =(r/ 180)XπXn

The central angle refers to the ∠AOB formed by the radii of the two ends of the arc AB on the circle with the center of O, which is called the central angle of the arc AB. The central angle is equal to twice the central angle of the same arc. The degree of the central angle is equal to the degree of the arc it faces.

Relationship with arc, chord and chord center distance

In the same circle or in the same circle, if one of two central angles, two arcs, two chords and the chord-center distance of two chords is equal, the corresponding other components are also equal.

Equal arc and equal central angle. When the vertex is divided into 360 parts at the corner of the center, the central angle of each part is 1. Because the arcs with equal central angles in the same circle are equal, the whole circle is divided into 360 parts equally. At this time, each arc thus obtained is called the arc of 1.

Extended data

Central angle characteristic

1, the vertex is the center of the circle;

2. Two sides intersect the circumference.

3. The nature of the central angle: in the same circle or in the same circle, the central angle of the circle has equal arc, chord and chord center distance. In the same circle or the same circle, as long as one of the four pairs is equal, the other three pairs must be equal. ?

The degree of arc is equal to the degree of the central angle it subtends.

5. The circumference angle (or diameter) of a semicircle is a right angle; A chord with a circumferential angle of 90 is a diameter.

6.s (sector area) = (n/360) x π R2;