Question 834662
<pre>
The sum of the measures of the exterior angles of any
polygon is 360°.  Since the 20-sided polygon is a regular 
polygon, all 20 exterior angles have the same measure,
so each is {{{"360°"/20}}} or 18° each.  The green lines
below form one exterior angle of the 20-sided polygon.
It's interesting that each exterior angle is congruent to
every central angle.  As you see below, each central angle 
also has measure 18°.
{{{drawing(400,400,-1.2,1.2,-1.2,1.2,locate(.4,.1,"18°"),
red(arc(0,0,1.1,-1.1,0,18)), red(arc(0,0,.7,-.7,0,18)),
red(arc(1,0,.7,-.7,81,99)), red(arc(1,0,1.1,-1.1,81,99)),
line(1,0,0.95105652,0.30901699),locate(.93,.5,"18°"),
line(0.95105652,0.30901699,0.80901699,0.58778525),
line(0.80901699,0.58778525,0.58778525,0.80901699),
line(0.58778525,0.80901699,0.30901699,0.95105652),
line(0.30901699,0.95105652,0,1),
line(0,1,-0.30901699,0.95105652),
line(-0.30901699,0.95105652,-0.58778525,0.80901699),
line(-0.58778525,0.80901699,-0.80901699,0.58778525),
line(-0.80901699,0.58778525,-0.95105652,0.30901699),
line(-0.95105652,0.30901699,-1,0),
line(-1,0,-0.95105652,-0.30901699),
line(-0.95105652,-0.30901699,-0.80901699,-0.58778525),
line(-0.80901699,-0.58778525,-0.58778525,-0.80901699),
line(-0.58778525,-0.80901699,-0.30901699,-0.95105652),
line(-0.30901699,-0.95105652,0,-1),
line(0,-1,0.30901699,-0.95105652),
line(0.30901699,-0.95105652,0.58778525,-0.80901699),
line(0.58778525,-0.80901699,0.80901699,-0.58778525),
line(0.80901699,-0.58778525,0.95105652,-0.30901699),
line(0.95105652,-0.30901699,1,0),
green(line(1,0,9,50.51001523),line(-4,31.56875952,.95105652,.30901699)),
line(1,0,0,0),
line(0.95105652,0.30901699,0,0),
line(0.80901699,0.58778525,0,0),
line(0.58778525,0.80901699,0,0),
line(0.30901699,0.95105652,0,0),
line(0,1,0,0),
line(-0.30901699,0.95105652,0,0),
line(-0.58778525,0.80901699,0,0),
line(-0.80901699,0.58778525,0,0),
line(-0.95105652,0.30901699,0,0),
line(-1,0,0,0),
line(-0.95105652,-0.30901699,0,0),
line(-0.80901699,-0.58778525,0,0),
line(-0.58778525,-0.80901699,0,0),
line(-0.30901699,-0.95105652,0,0),
line(0,-1,0,0),
line(0.30901699,-0.95105652,0,0),
line(0.58778525,-0.80901699,0,0),
line(0.80901699,-0.58778525,0,0),
line(0.95105652,-0.30901699,0,0) )}}}

Edwin</pre>