Question 892200
<pre>
Yes.  The sum of the exterior angles of any convex polygon is 360°.  Since this
is a regular polygon the polygon has all its exterior angles the same, so each
one would be {{{"360°"/n}}}, so we have the equation:

{{{"360°"/n}}}{{{""=""}}}{{{"8°"}}}

Multiply both sides by n

{{{"360°"}}}{{{""=""}}}{{{"8°n"}}}

Divide both sides by 8°

{{{"360°"/"8°"}}}{{{""=""}}}{{{n}}}

{{{45}}}{{{""=""}}}{{{n}}}

So it has 45 sides.  It looks like this figure below, without the
"spokes". Notice that the green lines are the extensions of two 
adjacent sides and the angle between those two green lines is an 
exterior angle of 8°.

{{{drawing(400,400,-1.3,1.3,-1.3,1.3,

green(line(-0.1391731,0.99026807,5,1.3496),line(0,1,5,.65037)),
line(0,1,-0.1391731,0.99026807),
line(-0.1391731,0.99026807,-0.27563736,0.9612617),
line(-0.27563736,0.9612617,-0.40673664,0.91354546),
line(-0.40673664,0.91354546,-0.52991926,0.8480481),
line(-0.52991926,0.8480481,-0.64278761,0.76604444),
line(-0.64278761,0.76604444,-0.74314483,0.66913061),
line(-0.74314483,0.66913061,-0.82903757,0.5591929),
line(-0.82903757,0.5591929,-0.89879405,0.43837115),
line(-0.89879405,0.43837115,-0.95105652,0.30901699),
line(-0.95105652,0.30901699,-0.98480775,0.17364818),
line(-0.98480775,0.17364818,-0.99939083,.034899497),
line(-0.99939083,.034899497,-0.9945219,-0.10452846),
line(-0.9945219,-0.10452846,-0.97029573,-0.2419219),
line(-0.97029573,-0.2419219,-0.92718385,-0.37460659),
line(-0.92718385,-0.37460659,-0.8660254,-0.5),
line(-0.8660254,-0.5,-0.78801075,-0.61566148),
line(-0.78801075,-0.61566148,-0.69465837,-0.7193398),
line(-0.69465837,-0.7193398,-0.58778525,-0.80901699),
line(-0.58778525,-0.80901699,-0.46947156,-0.88294759),
line(-0.46947156,-0.88294759,-0.34202014,-0.93969262),
line(-0.34202014,-0.93969262,-0.20791169,-0.9781476),
line(-0.20791169,-0.9781476,-.069756474,-0.99756405),
line(-.069756474,-0.99756405,.069756474,-0.99756405),
line(.069756474,-0.99756405,0.20791169,-0.9781476),
line(0.20791169,-0.9781476,0.34202014,-0.93969262),
line(0.34202014,-0.93969262,0.46947156,-0.88294759),
line(0.46947156,-0.88294759,0.58778525,-0.80901699),
line(0.58778525,-0.80901699,0.69465837,-0.7193398),
line(0.69465837,-0.7193398,0.78801075,-0.61566148),
line(0.78801075,-0.61566148,0.8660254,-0.5),
line(0.8660254,-0.5,0.92718385,-0.37460659),
line(0.92718385,-0.37460659,0.97029573,-0.2419219),
line(0.97029573,-0.2419219,0.9945219,-0.10452846),
line(0.9945219,-0.10452846,0.99939083,.034899497),
line(0.99939083,.034899497,0.98480775,0.17364818),
line(0.98480775,0.17364818,0.95105652,0.30901699),
line(0.95105652,0.30901699,0.89879405,0.43837115),
line(0.89879405,0.43837115,0.82903757,0.5591929),
line(0.82903757,0.5591929,0.74314483,0.66913061),
line(0.74314483,0.66913061,0.64278761,0.76604444),
line(0.64278761,0.76604444,0.52991926,0.8480481),
line(0.52991926,0.8480481,0.40673664,0.91354546),
line(0.40673664,0.91354546,0.27563736,0.9612617),
line(0.27563736,0.9612617,0.1391731,0.99026807),
line(0.1391731,0.99026807,0,1),

line(0,1,0,0),
line(-0.1391731,0.99026807,0,0),
line(-0.27563736,0.9612617,0,0),
line(-0.40673664,0.91354546,0,0),
line(-0.52991926,0.8480481,0,0),
line(-0.64278761,0.76604444,0,0),
line(-0.74314483,0.66913061,0,0),
line(-0.82903757,0.5591929,0,0),
line(-0.89879405,0.43837115,0,0),
line(-0.95105652,0.30901699,0,0),
line(-0.98480775,0.17364818,0,0),
line(-0.99939083,.034899497,0,0),
line(-0.9945219,-0.10452846,0,0),
line(-0.97029573,-0.2419219,0,0),
line(-0.92718385,-0.37460659,0,0),
line(-0.8660254,-0.5,0,0),
line(-0.78801075,-0.61566148,0,0),
line(-0.69465837,-0.7193398,0,0),
line(-0.58778525,-0.80901699,0,0),
line(-0.46947156,-0.88294759,0,0),
line(-0.34202014,-0.93969262,0,0),
line(-0.20791169,-0.9781476,0,0),
line(-.069756474,-0.99756405,0,0),
line(.069756474,-0.99756405,0,0),
line(0.20791169,-0.9781476,0,0),
line(0.34202014,-0.93969262,0,0),
line(0.46947156,-0.88294759,0,0),
line(0.58778525,-0.80901699,0,0),
line(0.69465837,-0.7193398,0,0),
line(0.78801075,-0.61566148,0,0),
line(0.8660254,-0.5,0,0),
line(0.92718385,-0.37460659,0,0),
line(0.97029573,-0.2419219,0,0),
line(0.9945219,-0.10452846,0,0),
line(0.99939083,.034899497,0,0),
line(0.98480775,0.17364818,0,0),
line(0.95105652,0.30901699,0,0),
line(0.89879405,0.43837115,0,0),
line(0.82903757,0.5591929,0,0),
line(0.74314483,0.66913061,0,0),
line(0.64278761,0.76604444,0,0),
line(0.52991926,0.8480481,0,0),
line(0.40673664,0.91354546,0,0),
line(0.27563736,0.9612617,0,0),
line(0.1391731,0.99026807,0,0)


  )}}}

Edwin</pre>