Measurement of Angles Formulas

Measurement of Angles Formulas

The concept of angle is one of the most important concepts in geometry. The whole concept of trigonometry relies on the concept of angles. Without the use of angles and it’s measurement geometry and trigonometry cannot be imagined.

The important formulas of angle’s measurement are listed below:-

1. One radian is written as $1^0$

2. One right angle = $90^\circ = 100^g = \dfrac{\pi}{2}$ radians, where $\pi^c = 180^\circ$

3. $1^\circ = (\dfrac{10}{9})^g = (\dfrac{\pi}{180})^c = \dfrac{1}{90}$ of a right angle.

4. $1^g = (\dfrac{9}{10})^\circ = (\dfrac{\pi}{200})^c = \dfrac{1}{100}$ of a right angle.

5. $1^c = (\dfrac{180}{\pi})^\circ = (\dfrac{200}{\pi})^g = \dfrac{2}{\pi}$ of a right angle.

6. The number of radian in an angle subtended by an arc of a circle at the centre, $\theta = \dfrac{arc}{radian}$ i.e. $\theta = \dfrac{l}{r}$ i.e. $l = \theta r$.

7. Exterior angle of a polygon of n sides = $\dfrac{360^\circ}{n}$ and interior angle of a polygon of n sides = $\dfrac{180^\circ(n- 2)}{n}$

8. Sum of interior angles of a polygon of n sides = $180(n- 2)^\circ$

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