Question 936376

Suppose the interior angle is {{{x}}} degrees.
Then the exterior angle is {{{180 - x}}} degrees.


{{{x = 5*(180-x)}}}

{{{x = 900 - 5x}}}

{{{6x = 900}}} 

{{{ x = 150}}} degrees.

So exterior angle = {{{30}}} degrees.

If the polygon has {{{n}}} sides (and n angles) the sum of its exterior angles is {{{30*n}}}

But the exterior angles of a polygon add to {{{360 }}} degrees
So, {{{30*n = 360}}} => {{{n = 12}}}.

ANSWER: the polygon has {{{12}}} sides.