Each of the interior angles of a regular polygon is 140o. How many sides has the polygon?
Answer Details
For a regular polygon with n sides, each interior angle is given by:
interior angle = (n-2) x 180 / n
We are given that each interior angle of the polygon is 140 degrees. Substituting this into the formula, we get:
140 = (n-2) x 180 / n
Multiplying both sides by n, we get:
140n = (n-2) x 180
Expanding the right-hand side, we get:
140n = 180n - 360
Simplifying and isolating n, we get:
n = 360 / (180 - 140)
n = 360 / 40
n = 9
Therefore, the regular polygon has 9 sides.
Hence, the answer to the question is 9.