if the difference in the degree measure of an interior and exterior angle of a regular polygon is 100 degree,how many sides doesthe poygon have??
To find the number of sides of a regular polygon given the difference in the degree measure of an interior and exterior angle, we can use the following formula:
n = 360 / (exterior angle - interior angle)
In this case, the given difference is 100 degrees. So, we can substitute the values into the formula:
n = 360 / (exterior angle - interior angle)
n = 360 / (x - (x + 100))
n = 360 / (-100)
Since the denominator is -100, we can flip the sign and divide:
n = 360 / 100
n = 3.6
However, since a polygon cannot have a fractional number of sides, we round the answer to the nearest whole number.
n ≈ 4
Therefore, the polygon has 4 sides.