Question 502196
In a regular polygon of n sides, the measure of an internal angle is given by:
{{{(n-2)180/n}}}
An internal angle and the corresponding external angle are complementary so that if the external angle is 20 degrees then the corresponding internal angle is 180-20 = 160 degrees.
{{{(n-2)180/n = 160}}} Solve for n.
{{{(n-2)180 = 160n}}} 
{{{180n-360 = 160n}}} Subtract 160n from both sides.
{{{20n-360 = 0}}} Add 360 to both sides.
{{{20n = 360}}} Divide by 20.
{{{n = 18}}}
The regular polygon has 18 sides.