A picture frame is shaped as a heptagon. The measure of one angle is 216°. The remaining interior angles are congruent. What is the measure of each remaining interior angle in the picture frame?

Question

anonymous · Answer

draw a heptagon roughly, and figure out how many triangles it can be divided into - turns out to be 5.
For each trianle the interior angles is 180, so total interior angles for the heptagon is 5*180=900

you know one of the angles is 216, so subtract thatfrom 900
6 remaining angles sum to 900-216=684

Given they are congruent that means the 6 angles are all equal, so each is 684/6 or 114 degrees. 

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