Quadrilateral: Interior Angles

How to solve the interior angles of a quadrilateral: formula, 1 example, and its solution.

Formula

Formula

m∠1 + m∠2 + m∠3 + m∠4 = 180

∠1, ∠2, ∠3, ∠4: Interior angles of a quadrilateral

Polygon: Interior Angles

Example

Example

Solution

These four angles
are the interior angles of the quadrilateral.

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

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

So 20x + 160 = 360.

Move +160 to the right side.

Then 20x = 200.

Divide both sides by 20.

Then x = 10.

So x = 10 is the answer.