Subject: Geometry

# Angle Classifications

### Angle

When two non-co-linear rays meet at a common end point it forms an "angle". The common endpoint is denoted as the "vertex", and the rays are the sides.

**\angle{ABC } with vertex at point B**

### Classification

**Acute angles** are angles that measures less than 90^{o}.

**acute angle**

**Right angles** are angles that measures 90^{p} exactly.

**Right angle**

**Obtuse angles** are angles that measures greater than 90^{o}.

**obtuse.jpg**

### Pairs of Angles

Angles are said to be ** complimentary** if the sum of it's angle measures is 90

^{o}.

45

^{o}+ 45

^{o}= 90

^{o}.

**Therefore \angle{ABC} and \angle{CBD} are**

**' of each other.***'compliments*Angles are said to be ** supplementary** of the sum of their angles is equal to 180

^{o}.

**45**

^{o}+ 135^{o}= 180^{o}. Therefore, \angle{ABD} and \angle{CBD} are*supplementary*.**'Complementray and supplementray angles may/ may have not a common side.'**

Angles are said to ** adjacent** if they have a common side (ray).

**\angle{ABC} is adjacent to \angle{CBD}**.

**Their common side is \overset{\rightarrow}{BC}**

When two angles have a common side, and the other sides are opposite rays,it will be called as *linear pair*

**\angle{ABC} and \angle{CBD} form a linear pair with \overset{\rightarrow}{BD} as their common side.**

If the sides of one angle are the opposite rays of another angle then these angles are called ** vertical angles**.

**\angle{PQT} and \angle{SQR} are vertical angles. \angle{SQP} and \angle{RQT} are also vertical angles.**