A quadrilateral in inscribed in a circle. If an angle is inscribed into each of the four segments outside the quadrilateral, the sum of the these four angles, expressed in degrees is :
1. Draw a sketch of the situation: You'll notice that you are dealing with an octogon. Calculate the sum of the interior angles of the octogon.
2. Now you take each second vertex and add the corresponding interior angle:
$\displaystyle \text{sum of additional angles}=\dfrac{\text{sum of interior angles of the octogon}}2$
Spoiler: