Skill: Find unknown angles in quadrilaterals

A quadrilateral is a shape with four sides and four interior angles. The angles inside every simple quadrilateral add to:

$$360^\circ$$

To find an unknown angle:

1. Add the known angles.
2. Subtract that total from $360^\circ$.
3. Write the answer with a degree symbol.

Example

A quadrilateral has angles measuring $90^\circ$, $105^\circ$, $80^\circ$, and $x^\circ$. Find $x$.

First, write an equation using the angle sum:

$$90^\circ+105^\circ+80^\circ+x^\circ=360^\circ$$

Add the known angles:

$$275^\circ+x^\circ=360^\circ$$

Subtract $275^\circ$ from both sides:

$$x^\circ=360^\circ-275^\circ$$ $$x=85^\circ$$

The unknown angle measures $85^\circ$.