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 :

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- Jun 25th 2010, 05:15 PMVeronica1999Quadrilateral
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 :

- Jun 25th 2010, 10:31 PMearboth
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:

$\displaystyle \text{sum of additional angles}=\dfrac{\text{sum of interior angles of the octogon}}2$

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