Question 1037922

The exterior angle of a regular polygon is one-third of its interior angle. How many sides has the polygon 
<pre>Let one of the exterior angles be E
Then one of the interior angles is: 3E
Since the exterior and interior angles are supplementary, we get: E + 3E = 180
4E = 180
E, or one of the EXTERIOR angles = {{{180/4}}}, or 45<sup>o</sup>
Since the exterior angles of any polygon sum to 360<sup>o</sup>, we can say that the number of sides of the polygon = {{{360/45}}}, or {{{highlight_green(8)}}}, thus making it an OCTAGON.