Each of the interior angles of a regular polygon is 140o. How many sides has the polygon?
Answer Details
The sum of the interior angles of a polygon can be found using the formula:
S = (n - 2) × 180o
where S is the sum of the interior angles, and n is the number of sides in the polygon.
For a regular polygon, all interior angles have the same measure. In this case, the interior angle of the polygon is given as 140o. Therefore, we can use the formula:
S = n × 140o
Substituting this into the formula for the sum of interior angles, we get:
n × 140o = (n - 2) × 180o
Simplifying this equation, we get:
140n = 180n - 360
Solving for n, we get:
40n = 360
n = 9
Therefore, the polygon has 9 sides. The answer is 9.