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 90o.


acute angle

Right angles are angles that measures 90p exactly.


Right angle

Obtuse angles are angles that measures greater than 90o.


obtuse.jpg

Pairs of Angles

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


45o + 45o = 90o. Therefore \angle{ABC} and \angle{CBD} are 'compliments' of each other.

Angles are said to be supplementary of the sum of their angles is equal to 180o.


45o + 135o = 180o. 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.