1982 AMC 12 第 6 题

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 $2750^\circ$ is $2700^\circ,$ leaving $2700^\circ-2570^\circ=130^\circ.$

Therefore, the correct answer is D.