Each of the interior angles of a regular polygon is 140°. How many sides has the polygon?
Question 1 Report
Each of the interior angles of a regular polygon is 140°. How many sides has the polygon?
Answer Details
A regular polygon is a polygon with equal sides and equal interior angles. The formula to find the interior angle of a regular polygon is given by:
(180 * (n-2)) / n,
where n is the number of sides in the polygon.
So, if each interior angle of a regular polygon is 140°, we can plug that value into the formula and solve for n:
140 = (180 * (n-2)) / n
Multiplying both sides by n gives:
140n = 180 * (n-2)
Expanding the right side gives:
140n = 180n - 360
Subtracting 140n from both sides gives:
0 = 40n - 360
Adding 360 to both sides gives:
360 = 40n
Dividing both sides by 40 gives:
n = 9
So, the polygon has 9 sides.
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