# Interior Angles of a Triangle

How to solve the interior angles of a triangle problems: formula, proof, example, and its solution.

## Formula

The sum of the measures of the interior angles of a triangle is 180.

## Proof

Draw an auxiliary line

that passes through the upper vertex

and that is parallel to the base.

Draw a green angle

on the left side of the blue angle.

The green angles are congruent

because they are

alternate interior angles in parallel lines.

Draw a red angle

on the right side of the blue angle.

By the same reason,

the red angles are also congruent.

The angles at the upper vertex

(green, blue, and red)

are on the auxiliary line.

So m∠(blue) + m∠(green) + m∠(red) = 180.

## Example

The colored angles are the interior angles of a triangle.

So (60) + (3*x* + 30) + (7*x* + 10) = 180.