Angles of the Triangle

In a triangle there are two kinds of angles:

Angles of the Triangle

The interior angles are formed by two sides.

The exterior angles are formed on one side and its extension.


Properties of the Angles of a Triangle

1. The sum of the interior angles of a triangle equals 180°.

A + B + C = 180º


2.  The value of an exterior angle of a triangle equals the sum of the two nonadjacent interior angles.

α = B + C


3.   The interior and exterior angles of a triangle at a particular vertex are supplementary, that is to say, they add up 180º.

α = 180º - A


Types of Triangles by Angles

Acute Triangle

Acute Triangle


An acute triangle has three acute angles.

Right Triangle

Right Triangle

A right triangle has a right angle.

The longest side of the triangle is called the hypotenuse.

The shorter sides of the triangle are the legs or catheti (singular: cathetus).

Obtuse Triangle

Obtuse Triangle


An obtuse triangle has an obtuse angle.