The interior angles of a quadrilateral have a sum of 360°
This can be demonstrated by tearing off the corners and showing that they fit together to form a revolution, or by drawing quadrilaterals and measuring the angles. But it can be proved.
The sum of the interior angles in a quadrilateral is 360°.
There are two kinds of quadrilaterals, as shown in the diagrams below. When one diagonal is drawn, two triangles are formed. The angle sum of each triangle is 180°. Hence the angle sum of the quadrilateral is 360°.
Find the value of θ in the following quadrilateral.
θ + 112° + 78° + 76° = 360°
Hence θ = 94°.