How many sides does the regular polygon have if each interior angle is the given amount:?

Question

144 degrees

120 degrees

140 degrees

Answer 1

total angle of a polygon = 180(n-2)

each interior angle of a regular polygon = 180(n-2)/n

144n = 180(n-2), n=10

120n = 180n - 360, n= 6

140n = 180n - 360, n=9

Answer 2

(n-2)(180) over n = 144

solve for n

180n - 360 = 144n

-360 = 144n - 180n

-360 = -36n

n = 10 sides

Answer 3

The measure of an interior angle of a regular polygon can be calculated by:

[180 x (n - 2)] / n

That's 180 times (n - 2) all divided by n, where n is the number of sides the polygon has.

For a regular polygon with interior angles of 144 degrees:

144 = [180 x (n - 2)] / n

144n = 180 x (n - 2)

144n = 180n - 360

-36n = -360

n=10

The polygon has 10 sides, it's a regular decagon.

Use this same method by plugging in 120 and 140  instead of 144 to get the next two answers. Good luck!

Answer 4

Break up the polygon in your head.  Maybe draw a picture of the polygon as a bunch of isosceles triangles that intersect at the center of the circle.  

If n stands for the number of sides on the polygon, the angle that goes out from the center is 360/n.  That means that the other two angles added together are the angle of the polygon.  And since they make up the angle of a triangle, they add to 180 degrees.  

So 120+360/n=180  

360/n=180-120=60

60*n=360

n=360/60=6

hexagon

So 140+360/n=180  

360/n=180-140=40

40*n=360

n=360/40=9

nonagon

So 144+360/n=180  

360/n=180-144=36

36*n=360

n=360/36=10

decagon

Answer 5

with "n" equaling the number of sides

180(n-2)=144n

180n-360=144n

36n=360

n=10

180(n-2)=120n

180n-360=120n

60n=360

n=6

180(n-2)=140n

180n-360=140n

40n=360

n=9