If the sum of all the angles except one of a convex polygon is 2190°, then the number of sides of the polygon must be

1973 AMC 12 Problem 16

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16.

If the sum of all the angles except one of a convex polygon is

2190^\circ,

then the number of sides of the polygon must be

13

15

17

19

21

Let the omitted interior angle be

x^\circ

and the number of sides be

n

Use

0\lt x\lt180

to trap the integer

n-2

in an interval of length

1

If the omitted angle is

x^\circ,

then convexity gives

0\lt x\lt180.

Hence

180(n-2)=2190+x,

\frac{2190}{180} \lt n-2 \lt\frac{2370}{180}.

This is

12\frac16\lt n-2\lt13\frac16.

The only possible integer is

n-2=13,

n=15.

Therefore, the correct answer is B.