Question 408195
Let {{{theta}}} be the measure of the exterior angle, and {{{3*theta}}} be the measure of the interior angle. These two must add to 180 degree (since they're a linear pair) so


{{{theta + 3*theta = 180}}} --> {{{theta = 45}}}, {{{3*theta}}} = 135.


Two ways to find the number of sides:


Solution 1:
If you know that the sum of the exterior angles of an n-gon is 360 degrees, and that in this case the exterior angle is 45 degrees, then the number of sides is 360/45 = 8.


Solution 2:
The sum of the measures of the interior angles of an n-gon is {{{180(n-2)}}}. Divide this by n to get the average measure. Since each interior angle measures 135, we have


{{{135 = 180(n-2)/n}}}, which can be solved to obtain {{{n = 8}}}.