Verified answer

The formula for the sum of the interior angles of a polygon is:

(n - 2)180° where n is the number of sides of the polygon.

By using the formula above, we have:

180(n - 2) = 1440 [Divide both sides by 180]

n - 2 = 1440/180

n - 2 = 8 [Add both sides by 2]

n = 8 + 2

n = 10

Hence, the polygon with the total measurement of 1440° is a decagon.

I hope this helps!

Internal Angles Of A Polygon

First derive a formula for how many degrees are in a regular shape:

A shape with n number of sides can be divided into n-2 triangles by connecting one corner with every other corner. For instance, if you take a square, and draw a diagonal, you will have 4 sides and 2 triangles.

Since a triangle has 180 degrees in it, you multiply this by n-2 to get the total number of degrees: Degrees = 180*(n-2). Again with the square, n = 4, so 180*(4-2) = 180*2 = 360, and we know that squares have 360 degrees. The formula works!

Now plug in 1440 to the equation for degrees, and you get 1440 = 180*(n-2).

Let's solve for that:

1440 = 180*(n-2)

1440/180 = (n-2)

1440/180 + 2 = n = 8 + 2 = 10

a 10 sided polygon, or a decagon

Sum of interior angles of a polygon is given by 180(n - 2), where n is the number of sides of the polygon. Setting the expression equal to 1440,

180(n - 2) = 1440 iff

n - 2 = 8 iff

n = 10

We see that the polygon has 10 sides, thus decagon.

Decagon. You just asked what sort of polygon had an interior angle of 144 degrees. 144 x 10 =1440.

a DECAGON.

1440 = 180(n-2)

8 = n-2

n = 10 (DECAGON)

Total internal angles = 180(n-2)

= 180 * (10 -2)

=1440

Compare 1440 to 180(n-2)....