The sum of the interior angles of a regular polygon is three times the sum of its exterior angles. The number of sides of the polygon is:
Question
The sum of the interior angles of a regular polygon is three times the sum of its exterior angles. The number of sides of the polygon is:
Solution
The sum of the interior angles of a polygon is given by the formula (n-2) * 180, where n is the number of sides.
The sum of the exterior angles of any polygon is always 360 degrees.
According to the problem, the sum of the interior angles is three times the sum of the exterior angles. So, we can set up the equation:
(n-2) * 180 = 3 * 360
Solving this equation will give us the number of sides of the polygon.
(n-2) * 180 = 1080
n - 2 = 1080 / 180
n - 2 = 6
n = 6 + 2
n = 8
So, the polygon has 8 sides.
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