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

Question 3181: Suppose the interior angles of a convex pentagon are five consecutive numbers, find the measure of the largest angle.
Found 2 solutions by longjonsilver, khwang:
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
a pentagon is 5-sided. A 5-sided figure can be divided into 3 triangles, so total interior angles of a pentagon = 3*180 = 540.

Let smallest angle be x. Next will then be x+1, then x+2 etc.

so we get: x + x+1 + x+2 + x+3 + x+4 = 540
5x + 10 = 540
5x = 530
x = 106

so largest angle is 106+4 = 110

jon.

Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
For any polygon with n sides, the total interior angles =
180(n-2) = 540 when n=5.
Assume the middle angle is x, the five angles are x-2,x-1,x,x+1.x+2
we have the sum of them is 5x.

Solve 5x =540,
so x = 108 and the largest angle is 108+2 =110 deg
Kenny
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