• June 25th 2010, 06:15 PM
Veronica1999
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 :

• June 25th 2010, 11:31 PM
earboth
Quote:

Originally Posted by Veronica1999
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:

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

Spoiler:
You should come out with 540°