Angles in Quadrilaterals

In a Nutshell

The four interior angles of any quadrilateral always add up to $360°$ .

A quadrilateral is any flat shape with four straight sides. No matter how the sides are arranged, the interior angles always sum to $360°$ .

Why? Draw a diagonal across any quadrilateral. It splits the shape into two triangles. Each triangle's angles sum to $180°$ , so the total is $180° + 180° = 360°$ .

To find a missing angle, add up the three known angles and subtract from $360°$ :

$\text{missing angle} = 360° - (\text{sum of known angles})$

Preset:

Drag the vertices to reshape the quadrilateral, then press Split to see the diagonal divide it into two triangles. Each triangle's angles sum to $180°$ , so the total is always $360°$ .

Watch it work

Question: A quadrilateral has angles $85°$ , $110°$ and $95°$ . Find the fourth angle.

Have a go

Q1. A quadrilateral has angles $90°$ , $90°$ and $90°$ . Find the fourth angle.

Q2. A parallelogram has one angle of $65°$ . Find the other three angles.

Q3. A trapezium has angles $72°$ , $108°$ and $108°$ . Find the fourth angle.

Q4. The angles in a quadrilateral are $x$ , $2x$ , $3x$ and $4x$ . Find $x$ .