Interior Angles of a Quadrilateral

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.

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

Find the value of x. The measures of the interior angles: 5x + 30, 12x, 3x + 40, and 90.

The colored angles are the interior angles of a quadrilateral.

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