Question

A quadrilateral is inscribed in a circle. If an angle is inscribed into each of the four segments outside the quadrilateral, the sum of these four angles, expressed in degrees, is:
Ans is 540°.
Need solution!

Answer 1

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:

sum of additional angles=sum of interior angles of the octogon/2

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