# Angle Formula

Angle is formed when two rays intersect i.e. half-lines projected with a common endpoint. The corner points of angle is known as the vertex of the angle and the rays as the sides, i.e. the lines are known as the arms. It is defined as the measure of turn between the two lines. The unit of angle is radians or degrees. There are different types of formulas for angles some of them are double-angle formula, half angle formula, compound angle formula, interior angle formula etc.

Central Angle Formula =

$\large Angle = \frac{Arc\: Length \times 360}{2\pi Radius}$

Formula for Central Angle

$\large s = r\theta$

Where, s represents the arc length,
S = rθ
represents the central angle in radians and r is the length of the radius.

Formula for Double Angle

$\large \cos (2a) = \cos ^{2}(a) – \sin ^{2}(a) = 2 \cos ^{2}(a) -1 = 1-2\sin ^{2}(a)$
$\large \sin (2a) = 2\sin (a)\cos (a)$
$\large \tan (2a) = \frac{2\tan(a)}{1-\tan ^{2}(a)}$

### Solved Examples

Question 1: Find the angle of a segment in a circle if the arc length is 5π and the radius is 6 ?
Solution:

The angle formula is given as,Angle = $\frac{Arc Length \times 360}{2 \times \pi \times Radius}$

Angle = $\frac{5 \pi \times 360}{2 \times \pi \times 6}$ degrees

Angle = 150 degrees
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