Interior Angles of a Quadrilateral

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.

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

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.

5x + 12x + 3x = 20x
30 + 40 + 90 = 160

Move +160 to the right side.

Then 20x = 200.

Divide both sides by 20.

Then x = 10.