# Interior Angles of a Quadrilateral

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

## Formula

For a quadrilateral,

the sum of the measures of the interior angles is

360.

This is true because,

for an *n*-gon,

the sum of the measures of the interior angles is

180(*n* - 2).

And for a quadrilateral, *n* = 4.

So (sum) = 180(4 - 2)

= 360.

Interior angles of a polygon

## Example

The colored angles are

the interior angles of a quadrilateral.

So [5*x* + 30] + [12*x*] + [3*x* + 40] + [90] = 360.

5*x* + 12*x* + 3*x* = 20*x*

30 + 40 + 90 = 160

Move +160 to the right side.

Then 20*x* = 200.

Divide both sides by 20.

Then *x* = 10.