Question 3298
The formula for finding the interior angles of a regular polygon is:<br>

{{{I = 180 - (360/n)}}}, where n is the number of sides.<br>

The exterior angle is found by:<br>
{{{E = 180 - I}}}.<br>
If we replace I with the formula for interior angles into this equation we get:

{{{E = 180 - (180 - (360/n)) = 360/n}}}.<br>

We know E = 40 from the problem statement, so {{{n = (360/40) = 9 }}}