1982 AMC 12 Problem 6

Attempt Problem 6 of the 1982 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1982 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

The sum of all but one of the interior angles of a convex polygon equals

2570^\circ.

The remaining angle is

90^\circ

105^\circ

120^\circ

130^\circ

144^\circ

A polygon’s total interior angle sum is a multiple of

180^\circ

The missing convex angle must place the total strictly between

2570^\circ

and

2750^\circ

The total must be

(n-2)180^\circ

and the missing angle lies between

0^\circ

and

180^\circ.

The only multiple of

180^\circ

between

2570^\circ

and

2750^\circ

2700^\circ,

leaving

2700^\circ-2570^\circ=130^\circ.

Therefore, the correct answer is D.

Problem 6 in other years