# Interior Angles of a Quadrilateral

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

## Formula

The sum of the measures of the interior angles of a quadrilateral is 360.

This is true because

the interior angles of an *n*-gon is 180(*n* - 2)º.

And for a quadrilateral, *n* = 4.

So (sum) = 180(4 - 2) = 360.

## Example

The colored angles are the interior angles of a quadrilateral.

So (5*x* + 30) + (12*x*) + (3*x* + 40) + (90) = 360.