SOLUTION: Suppose the interior angles of a convex pentagon are five consecutive numbers, find the measure of the largest angle.

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Question 3298: Suppose the interior angles of a convex pentagon are five consecutive numbers, find the measure of the largest angle.
Answer by drglass(89) About Me  (Show Source):
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The formula for finding the interior angles of a regular polygon is:

I+=+180+-+%28360%2Fn%29, where n is the number of sides.

The exterior angle is found by:

E+=+180+-+I.

If we replace I with the formula for interior angles into this equation we get:
E+=+180+-+%28180+-+%28360%2Fn%29%29+=+360%2Fn.

We know E = 40 from the problem statement, so n+=+%28360%2F40%29+=+9+