# Angles of the Triangle

In a triangle there are two kinds of angles:

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

An acute triangle has three acute angles.

#### 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

An obtuse triangle has an obtuse angle.