Question 14620
The exterior angle of a regular polygon is the supplement of its interior angle.

The interior angle of a regular polygon is given by:
 {{{A = ((n-2)180)/n}}} where: n is the number of sides of the regular polygon.

1) You can write:

{{{180-((n-2)180)/n = 18}}} simplify and solve for n, the number of sides.
{{{(180n - 180n + 360)/n = 18}}} Multiply both sides by n
{{{180n - 180n + 360 = 18n}}}
{{{360 = 18n}}} Divide both sides by 18.
{{{n = 20}}} sides.

2) Use the formula for the interior angle of a regular polygon.

{{{((n-2)180)/n = 135}}} Simplify and solve for n.
{{{(180n - 360)/n = 135}}} Multiply both sides by n
{{{180n - 360 = 135n}}} Add 360 to both sides.
{{{180n = 135n + 360}}} Subtract 135n from both sides.
{{{45n = 360}}} Divide both sides by 45
{{{n = 8}}} sides.