The measure of an interior angle of a regular n-gon is 140 degree. How many sides are in the regular polygon?
let the number of sides be n
180(n-2)/n = 140
180n - 360 = 140n
40n = 360
n = 9
9-sided regular polygon, a nonagon
To find the number of sides in a regular polygon when given the measure of an interior angle, we can use the formula:
Number of sides (n) = 360 degrees / measure of interior angle
In this case, the measure of the interior angle is 140 degrees.
So, plugging in the values into the formula:
n = 360 degrees / 140 degrees
n ≈ 2.5714 (approximately)
Since the number of sides must be a whole number for a regular polygon, we need to round our answer to the nearest whole number.
Rounding to the nearest whole number, we find that the regular polygon has 3 sides.
Therefore, the regular polygon in question has 3 sides.