one of the interior angles of a regular polygon is 144degrees find the number of sides of the polygon

sum of angles=(180)(n-2)

each angle=sum/n = 180(n-2)/n

144n=180(n-2)
144n=180n-360
n=10

To find the number of sides of a regular polygon given the measure of one of its interior angles, you can use the formula:

n = 360 / x

Where "n" represents the number of sides and "x" is the measure of one interior angle.

In this case, you are given that one of the interior angles of the polygon is 144 degrees. Applying the formula, we get:

n = 360 / 144

Dividing 360 by 144 gives you:

n ≈ 2.5

However, a polygon cannot have a fractional number of sides. Therefore, we need to round to the nearest whole number. In this case, rounding up gives:

n = 3

The number of sides of the polygon is 3.