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1080° (as for any octagon)
"The sum of the interior angles of a simple n-gon is "(n − 2)π radians" or "(180n − 360)degrees". This is because any simple n-gon can be considered to be made up of (n − 2) triangles, each of which has an angle sum of π radians or 180 degrees. The measure of any interior angle of a convex regular n-gon is "(1 -(2/n))π radians" or "(180 - (360/n)) degrees". "
Source and further information:
http://en.wikipedia.org/wiki/Polygon#Angles
Further information:
http://en.wikipedia.org/wiki/Octagon
Hmm, Well each angle is 180-45 = 135. There are 8, so its 8 x 135 = 1080 deg or 18.85 radians
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