Question 1210519
<pre>
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.

The exterior angles of any polygon, sum to {{{360^o}}}. Therefore, each exterior angle of any regular polygon will be {{{360/n}}},
with n being the number of sides

Since it's stated that each interior angle is TWICE each exterior angle, then each interior angle of this regular polygon = {{{2(360/n)}}} = {{{720/n}}}.

Since the 2 angles (interior and exterior) are on a straight line, they are supplementary. This gives us: {{{360/n + 720/n = 180}}}
                                                                                                          360 + 720 = 180n ---- Multiplying by LCD, n
                                                                                                              1,080 = 180n
                                                           Number of sides that this regular polygon contains, or {{{n = "1,080"/180 = 6}}}

The regular polygon contains 6 sides, and is therefore, a <font color = red><font size = 4><b>regular HEXAGON</font></font></b>!

<font color = red><font size = 4><b>OR</font></font></b>

Let each exterior angle, be E
Then each interior angle = 2E
As these 2 angles are supplementary, we get: E + 2E = 180
                                                 3E = 180
Measure of each exterior angle of this regular polygon, or E = {{{180/3 = 60^o}}}.
As each exterior angle is {{{60^o}}}, and the sum of the exterior angles of any polygon is {{{360^o}}}, number of sides of this polygon = {{{360/60 = 6}}}
With 6 sides, this makes this a <font color = red><font size = 4><b>regular HEXAGON</font></font></b>!</pre>