Angles of a Quadrilateral

A quadrilateral has four angles inside it, one at each vertex. To find what they add up to, draw a diagonal that lies inside it. It cuts the quadrilateral into two triangles.

Here the diagonal AC makes triangles ABC and ACD, and the angles of each triangle add up to 180°. Together the six triangle angles fill the four corners exactly: at A and at C the diagonal splits the corner into two pieces, and the pieces add back up to the whole corner.

So the four angles of any quadrilateral add up to 2 × 180° = 360°, whatever its shape. This is the rule Angles in a polygon.