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.

parmen Apr 28, 2024

#2**+1 **

In any polygon, the sum of the interior angle and the exterior angle at a vertex is 180^{o}.

In this polygon, the value of the interior angle is twice that of the exterior angle,

therefore, the interior angle is 120^{o} and the exterior angle is 60^{o}. .

In any regular polygon, the sum of all the exterior angles is 360^{o}

irrespective of the number of vertexes.

Since one exterior angle of this polygon is 60^{o}

there must be six of them to total of 360^{o}.

We shall presume that there are the same number of sides that there are vertexes.

Therefore, this polygon has **six sides**.

**.**

Bosco Apr 28, 2024