Help with math?? Please. (10 points)

1. The sum of the interior angles of a regular polygon is 1800 . What is the measure of each exterior angle of the polygon?

2. What is the measure of one exterior angle of a regular 30 -sided polygon?

3.The sum of the interior angles of a regular polygon is 3420 . How many vertices does the polygon have?

1. The formula regarding angle sums is (angle sum)=(n-2)180 where n is the number of sides of the polygon. So for question one create the equation

1800=(n-2)180
10=n-2. Divide both sides by 180
12=n. Add 2 to both sides
You now know the polygon has 12 sides

Divide 1800 (angle sum) by 12 (again the number of sides) to get 150 as the degree of each interior angle. Subtract 150 from 360 to get 210 as the exterior angle (your answer)

2. Again use the formula

Y=(n-2)180
Y=(30-2)180
Y=5040
5040 is the total sum. Now divide that by the number of sides (30) to get 168 as the interior angle. Again subtract that from 360 to get your answer 192 degrees.

3. This time the sum is 3420. Put that into the formula

3420=(n-2)180
19=n-2
21=n

We now know that the polygon has 21 sides and thus 21 vertices because the number of vertices and sides are always equal on polygons. Answer 21.

Hope this helps

The sum of all the exterior angles of a polygon is always 360.

The sum of the interior angles is 180(n - 2), where is the number of sides the polygon has.

(1) 1800 = 180(n-2)
Solve for n and then do 360 / n to get your answer.

(2) 360 / 30 = 12

(3) 3420 = 180(n-2)
n = number of sides = number of vertices