Answer:
n = 9
Explanation:
The formula for calculating the interior angles of a regular polygon is:
Interior angle = (n - 2) * 180 / n
where n is the number of sides in the polygon.
Given that the interior angle of the regular polygon is measured as 140 degrees, we can plug this value into the formula and solve for n:
140 = (n - 2) * 180 / n
Multiplying both sides of the equation by n to eliminate the fraction, we get:
140n = (n - 2) * 180
Expanding the right-hand side of the equation, we get:
140n = 180n - 360
Adding 360n to both sides of the equation, we get:
140n + 360 = 180n
Subtracting 140n from both sides of the equation, we get:
360 = 40n
Dividing both sides of the equation by 40, we get:
n = 9
So, the regular polygon has 9 sides.