Sum of Angles.

• The sum of all angles in the 4 triangles is $4 \times 180 = 720^{\circ}$
• The sum of angles in the quadrilateral is $360^{\circ}$
• Each angle of the quadrilateral is vertically opposite to the ones in triangle
• $\therefore \text{Sum } = 720^{\circ} - 360^{\circ} = \boxed{360^{\circ}}$

We can see that the angle sum in blue triangle is the angle sum of the quadrilateral.

We note that the sum of the orange angles is the sum of sums of angles of four triangles minus $a+b+c+d$ and $a+b+c+d$ is equal to the sum of angles of a quadrilateral which is $360^\circ$ . Therefore, the sum of the orange angles $=4\times 180^\circ - (a+b+c+d) = 4\times 180^\circ - 360^\circ = \boxed{360}^\circ$ .

By the triangle exterior angle theorem, the sum of the orange angles are the sum of the green angles labelled below:

The green angles are the exterior angles of the center quadrilateral, which always has an exterior angle sum of $\boxed{360°}$ .