Angles Of Triangles - How many angles does a triangle have? (Examples) - BYJUS

# Angles of Triangles

Triangles are polygons made up of three sides, three vertices, and three angles. There are some special properties related to the interior angles and exterior angles of a triangle. We will learn to use these properties to find unknown angles in a triangle with the help of some examples....Read MoreRead Less

## What is a Triangle?

A triangle is a two-dimensional closed shape with three sides, three angles, and three vertices. A triangle is also a polygon.

The triangle shown above is abbreviated as $$\triangle$$ABC.

## What are Interior Angles?

Interior angles are the angles that exist within a polygon. Other angles form when the sides of a polygon are extended.

## What are Exterior Angles?

Exterior angles like the name suggests are the angles on the outside of the polygon that are adjacent to the interior angles.

## Measurement of the Interior Angles of a Triangle

The sum of a triangle’s interior angle measurements is $$180^\circ$$.

$$x^\circ$$ + $$y^\circ$$ + $$z^\circ$$ = $$180^\circ$$

Example:

Determine the interior angle’s measurement.

Solution:

We know that the sum of the interior angles of a triangle measure  degree

x + 20 + 80 = 180

x + 100 = 180

x = 80

As a result, the interior angles are 80, 80, and 20 degrees.

## Measurement of the Exterior Angles of a Triangle

The sum of the measures of the two nonadjacent interior angles equals the measure of a triangle’s exterior angle. In other words, the exterior angle is the sum of its opposite interior angles.

$$x^\circ$$ + $$y^\circ$$ = $$z^\circ$$

Example:

Determine the exterior angle’s measurement.

Solution:

Exterior angle is the sum of the opposite interior angles.

2 x = (x -5) + 80

2 x = x + 75

x = 75

As a result, the exterior angle measurement is $$2(75)^\circ$$ = $$150^\circ$$.

## Solved Examples

Example 1:

Determine the interior angle’s measurement.

x + 30 + 90 = 180

x + 120 = 180

x = 60

As a result, the interior angles are 60, 30, and 90 degrees.

Example 2:

Determine the exterior angle’s measurement.

= 50 + 30

z = 80

As a result, the exterior angle measurement is $$80^\circ$$

Example 3:

Emma is making a wooden birdhouse in the shape of a triangle. What is the measurement of the third angle if two of the interior angles measure

$$45^\circ$$ and $$63^\circ$$?

Solution:

We know that the sum of a triangle’s angles is 180.

Sum of interior angles of a triangle = Angle 1 + Angle 2 + Angle 3

$$180^\circ$$ = $$45^\circ$$ + $$63^\circ$$  Angle  3

Angle 3 = $$180^\circ$$ – ($$45^\circ$$ + $$63^\circ$$)

Angle 3 = $$72^\circ$$

The third angle is $$72^\circ$$.