You can put this solution on YOUR website! Drawing segments from one vertex to all the other vertices such that the segments are through the interior of the polygon will create several triangles. The sum of the measure of interior angles of these triangles will be the sum of the measures of the polygon's interior angles. ONE triangle has 180 degree for the sum of its interior angles, so,
Six triangles. Making a test drawing you can find that this corresponds to a polygon of 8 sides, so OCTAGON.
Also means 8 interior angles. How many degrees is one of these interior angles? degrees.
Taking one vertex, extend one side and you have two angles: An exterior angle adjascent to the interior angle and their sum is 180 degrees. They are supplementary.
What is the measure of just one exterior angle?
{exteriorAngle}+135=180
exteriorAngle=180-135=45
The sum of the exterior angles in just one direction will be , but from both directions around the octagon will be degrees.
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