Question

The sum of the interior angles of a regular polygon is 1800 degrees. What is the measure of each exterior angle of the polygon?
A. 150 degrees
B. 108 degrees
C. 60 degrees
D. 30 degrees

Answer 1

First you need to find how many sides the polygon has, so you use:
Sum of the measures of the interior angles of a polygon formula = 180(n - 2)
With n being number of sides

Plug in what you know
1800 = 180(n - 2)

Solve
1800 = 180n - 360
2160 = 180n
12 = n
n = 12

Next you find the measure of one interior angle, using

m=
With m being the measure of an interior angle

Plug in what you know

m = 180(12 - 2)/12

Solve
m = 180(10)/12
m = 1800/12
m = 150

So each interior angle = 150 degrees.

Since an interior angle + an exterior angle = 180 degrees, just subtract:
180
- 150
-----
30

So the answer ends up being 30 degrees.