SOLUTION: the sum of the interior angles of a convex polygon is 1080 (a)how many sides does the polygon have, (b)suppose the polygon is reular, what is the measure of each interior angles?

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Question 859614: the sum of the interior angles of a convex polygon is 1080 (a)how many sides does the polygon have, (b)suppose the polygon is reular, what is the measure of each interior angles?
Answer by jim_thompson5910(35256) About Me  (Show Source):
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a)


S = 180(n-2)


1080 = 180(n-2)


1080/180 = n-2


6 = n-2


6 + 2 = n


8 = n


n = 8


There are 8 sides.


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b)


Divide the sum 1080 by 8 to get 1080/8 = 135


Each interior angle is 135 degrees. This is if the polygon is regular.


Note: this is a regular octagon.