The measures of the interior angles of a convex polygon are in arithmetic progression. If the smallest angle is 100° and the largest angle is 140°, then the number of sides the polygon has is

1976 AMC 12 Problem 14

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14.

The measures of the interior angles of a convex polygon are in arithmetic progression. If the smallest angle is

100^\circ

and the largest angle is

140^\circ,

then the number of sides the polygon has is

6

8

10

11

12

The average of an arithmetic progression is the average of its first and last terms

Equate

120n

with the interior-angle sum

180(n-2)

The average angle is

\frac{100+140}{2}=120^\circ,

so the angle sum is

120n.

A convex

n

-gon has angle sum

180(n-2),

hence

120n=180(n-2)

and

n=6.

Therefore, the correct answer is A.