Angles

An angle can be defined as two rays sharing a common vertex.

Measurement of angles
An angle is measured by considering the ratio of an arc to the radius of the arc. A scaling constant k is multiplied for various units.
 * $$\theta=\frac{s}{r}(k)$$°

Units of measurement
There are various units of measurement for measuring angles, however the most commonly used are degrees or radians. "1° = 60' (60 arcminutes) = 3600' (3600 arcseconds)"
 * Degrees - It is denoted by a small circle as a superscript (°). One full rotation is considered equal to 360 degrees. Degree is subdivided into minutes and seconds as:-
 * Radians - This is a number and is dimensionless. A full circle is equal to $$2\pi$$ (pronounced two pi) radians. This in conjunction with the formula for arc length defines the historically famous irrational number $$\pi$$ (pronounced pi) as,
 * $$\pi=\frac{1}{2}\frac{circumference~of~a~circle}{radius~of~the~circle}$$

There are six types of angles: Acute, Obtuse, Straight, Right, Reflex and Complete.
 * 1) An Acute angle is less than 90° and more than 0°
 * 2) An Obtuse angle is more than 90° and less than 180°
 * 3) A Straight angle is 180°.
 * 4) A Right angle is 90°.
 * 5) A Reflex angle is more than 180°.
 * 6) A Complete angle is 360°.

Apart from those six types of angles, we have two types of relative angles namely complementary angles and supplementary angles.
 * 1) Complementary angles are the pair of angles whose sum is equal to a right angle.
 * 2) Supplementary angles are the pair of angles whose sum is equal to a straight angle.