The formula for calculating the measure of each interior angle of a regular polygon is:
Interior angle = (n-2) x 180° / n
where n is the number of sides of the polygon.
We are given that one of the interior angles measures 140 degrees. Therefore, we can set up the equation:
140 = (n-2) x 180° / n
To solve for n, we can first cross-multiply to eliminate the fraction:
140n = (n-2) x 180°
Distribute the 180° term:
140n = 180n - 360°
Add 360° to both sides:
140n + 360° = 180n
Subtract 140n from both sides:
360° = 40n
Divide both sides by 40:
n = 9
Therefore, the regular polygon has 9 sides.