+1537 In a certain regular polygon, the measure of each interior angle is $2$ times the measure of each exterior angle. Find the number of sides in this regular polygon.
+1239
In any polygon, the sum of the interior angle and the exterior angle at a vertex is 180o.
In this polygon, the value of the interior angle is twice that of the exterior angle,
therefore, the interior angle is 120o and the exterior angle is 60o. .
In any regular polygon, the sum of all the exterior angles is 360o
irrespective of the number of vertexes.
Since one exterior angle of this polygon is 60o
there must be six of them to total of 360o.
We shall presume that there are the same number of sides that there are vertexes.
Therefore, this polygon has six sides.
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