Question 865487: The measures of the interior angles of a convex octagon increase by 10 degrees for each angle what is the measure of the largest angle. I tried finding the measure of the interior angle of a regular octagon and I found out that it is 135 degrees. Then, I thought that if I added these numbers (135,145,125,155,115,165,105175) that it might solve the problem, but it was incorrect.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! An octagon has 8 sides and the sum of the interior angles of a convex octagon is
(8-2)(180) = 1080 degrees
also our convex polygon has no angle pointing inward, that is, no interior angle is greater than 180 degrees
our formula is
(x+10) + (x+20) +(x+30) + (x+40) + (x+50) + (x+60) + (x+70) + (x+80) = 1080
8x + 360 = 1080
8x = 720
x = 90
therefore our interior angles are
100, 110, 120, 130, 140, 150, 160, 170
and the largest interior angle is 170 degrees
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