In what polygon is the sum of the measures of the angles of the polygon equal to twice the sum of the measures of the exterior angels?
Question
In what polygon is the sum of the measures of the angles of the polygon equal to twice the sum of the measures of the exterior angles?
Solution
The sum of the measures of the exterior angles of any polygon is always 360 degrees.
The sum of the measures of the interior angles of a polygon can be found using the formula (n-2) * 180 degrees, where n is the number of sides of the polygon.
Given that the sum of the interior angles is twice the sum of the exterior angles, we can set up the equation:
(n-2) * 180 = 2 * 360
Solving for n gives:
(n-2) * 180 = 720
n-2 = 720 / 180
n-2 = 4
n = 4 + 2
n = 6
So, the polygon in which the sum of the measures of the angles of the polygon is equal to twice the sum of the measures of the exterior angles is a hexagon.
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