# Central Angle

A central angle is an angle whose apex (vertex) is the center of a circle O and whose leg (sides) are radii two distinct points in the circle A and B. The central angles are subtended by the intersecting an arc between those two points, and the arc length is the mid-angle of a circle of radius a (measured in radians ). The central angles is also known as the angular distance of the arc .

The size of the central angle is 0° < < 360° or 0 < < 2π ( radians). When defining or drawing a central angle, in addition to specifying the points A and B , one must specify whether the angle being defined is a convex angle (<180°) or a reflex angle (>180°). Equally, one has to specify whether the movement from point A to point B is clockwise or counter-clockwise.

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If the point of intersection of the legs of the angle A and B with the circle form a diameter , then = 180° is a right angle . (In radians, = .)

Let L be the minor arc of the circle between points A and B , and let R be the radius of the circle.

If the central angles is subtended by L , then

0^{\circ} < \Theta < 180^{\circ} \, , \,\, \Theta = \left( {\frac{180L}{\pi R}} \right) ^{\circ}=\frac{L}{R}.

(for degrees) Proof: The circumference of a circle with radius r is 2π r , and the arc minor L is (Θ/360°) the proportionate part of the entire circumference (see arc ). therefore:

L=\frac{\Theta}{360^{\circ}} \cdot 2 \pi R \, \Rightarrow \, \Theta = \left( {\frac{180L}{\pi R}} \right) ^{\circ}.

(for radians) Proof: The circumference of a circle with radius r is 2π r , and the arc minor L is (Θ/2π) the proportionate part of the entire circumference (see arc ). therefore

L=\frac{\Theta}{2 \pi} \cdot 2 \pi R \, \Rightarrow \, \Theta = \frac{L}{R}.

If the central angle is not subtended by a minor arc L , then is a reflex angles and

180^{\circ} < \Theta < 360^{\circ} \, , \,\, \Theta = \left( 360 - \frac{180L}{\pi R} \right) ^{\circ}=2\pi-\frac{L}{R}.

If a tangent at A and a tangent B intersect at the external point P , then as denoting the center O, the angles Boa ( convex ) and BPA are supplementary ( sum to 180°).

central angle of a regular polygon

A regular polygon with n sides is a bounded circle on which all its vertices lie and the center of the circle is also the center of the polygon. The central angle of a regular polygon is formed by the radii of two adjacent vertices at the centre. The measure of this angle is

2\pi/n.

Can one measure the central angle 90?

Solution: Larry cuts the circle into four equal parts. Therefore, the central angles of the quadrilateral is 90°. Example 3: Sally draws an arc 8 inches long and its central angle measures 120 degrees.

What is 90 degrees?

Right Angle – Right angle is the easiest to grasp and understand. This is the smoothest and easiest angle. It looks like the letter L of English. Its measurement is 90 degrees.

What is the angle of 180 called?

An angle of 180° is called a straight angle or a straight angle.

How to find the central angle?

A central angle is an angles whose apex (vertex) is the center of a circle O and whose leg (sides) are radii two distinct points in the circle A and B. The central angles are subtended by the intersecting an arc between those two points, and the arc length is the mid-angles of a circle of radius a (measured in radians).

How many arms are there in the fast?

It has four sides and four corners. Its opposite sides are of equal length. Triangle • It has three sides and three vertices (vertex).