Question 1005007
<pre>
The sum of the interior angles of any polygon with n sides is
{{{(n-2)}}}{{{"×"}}}{{{"180°"}}}

In this case n = 72, so we substitute

{{{(72-2)}}}{{{"×"}}}{{{"180°"}}}
 
{{{70}}}{{{"×"}}}{{{"180°"}}}

{{{"12600°"}}}

Since the polygon is regular, all 72 interior angles are
equal in measure, so we divide by 72 to find what each
interior angle measures:

{{{"12600°"/72}}}{{{""=""}}}{{{"175°"}}}

Ever seen a regular 72-gon?  Here's one. Notice that it looks
almost like a circle, but if you look carefully, you'll see
that the sides are straight.   [Some look jagged but that's
because of the pixels on your screen].

{{{drawing(800,800,-1.2,1.2,-1.2,1.2,

line(1,0,0.9961947,0.087155743),
line(0.9961947,0.087155743,0.98480775,0.17364818),
line(0.98480775,0.17364818,0.96592583,0.25881905),
line(0.96592583,0.25881905,0.93969262,0.34202014),
line(0.93969262,0.34202014,0.90630779,0.42261826),
line(0.90630779,0.42261826,0.8660254,0.5),
line(0.8660254,0.5,0.81915204,0.57357644),
line(0.81915204,0.57357644,0.76604444,0.64278761),
line(0.76604444,0.64278761,0.70710678,0.70710678),
line(0.70710678,0.70710678,0.64278761,0.76604444),
line(0.64278761,0.76604444,0.57357644,0.81915204),
line(0.57357644,0.81915204,0.5,0.8660254),
line(0.5,0.8660254,0.42261826,0.90630779),
line(0.42261826,0.90630779,0.34202014,0.93969262),
line(0.34202014,0.93969262,0.25881905,0.96592583),
line(0.25881905,0.96592583,0.17364818,0.98480775),
line(0.17364818,0.98480775,0.087155743,0.9961947),
line(0.087155743,0.9961947,0,1),
line(0,1,-0.087155743,0.9961947),
line(-0.087155743,0.9961947,-0.17364818,0.98480775),
line(-0.17364818,0.98480775,-0.25881905,0.96592583),
line(-0.25881905,0.96592583,-0.34202014,0.93969262),
line(-0.34202014,0.93969262,-0.42261826,0.90630779),
line(-0.42261826,0.90630779,-0.5,0.8660254),
line(-0.5,0.8660254,-0.57357644,0.81915204),
line(-0.57357644,0.81915204,-0.64278761,0.76604444),
line(-0.64278761,0.76604444,-0.70710678,0.70710678),
line(-0.70710678,0.70710678,-0.76604444,0.64278761),
line(-0.76604444,0.64278761,-0.81915204,0.57357644),
line(-0.81915204,0.57357644,-0.8660254,0.5),
line(-0.8660254,0.5,-0.90630779,0.42261826),
line(-0.90630779,0.42261826,-0.93969262,0.34202014),
line(-0.93969262,0.34202014,-0.96592583,0.25881905),
line(-0.96592583,0.25881905,-0.98480775,0.17364818),
line(-0.98480775,0.17364818,-0.9961947,0.087155743),
line(-0.9961947,0.087155743,-1,0),
line(-1,0,-0.9961947,-0.087155743),
line(-0.9961947,-0.087155743,-0.98480775,-0.17364818),
line(-0.98480775,-0.17364818,-0.96592583,-0.25881905),
line(-0.96592583,-0.25881905,-0.93969262,-0.34202014),
line(-0.93969262,-0.34202014,-0.90630779,-0.42261826),
line(-0.90630779,-0.42261826,-0.8660254,-0.5),
line(-0.8660254,-0.5,-0.81915204,-0.57357644),
line(-0.81915204,-0.57357644,-0.76604444,-0.64278761),
line(-0.76604444,-0.64278761,-0.70710678,-0.70710678),
line(-0.70710678,-0.70710678,-0.64278761,-0.76604444),
line(-0.64278761,-0.76604444,-0.57357644,-0.81915204),
line(-0.57357644,-0.81915204,-0.5,-0.8660254),
line(-0.5,-0.8660254,-0.42261826,-0.90630779),
line(-0.42261826,-0.90630779,-0.34202014,-0.93969262),
line(-0.34202014,-0.93969262,-0.25881905,-0.96592583),
line(-0.25881905,-0.96592583,-0.17364818,-0.98480775),
line(-0.17364818,-0.98480775,-0.087155743,-0.9961947),
line(-0.087155743,-0.9961947,0,-1),
line(0,-1,0.087155743,-0.9961947),
line(0.087155743,-0.9961947,0.17364818,-0.98480775),
line(0.17364818,-0.98480775,0.25881905,-0.96592583),
line(0.25881905,-0.96592583,0.34202014,-0.93969262),
line(0.34202014,-0.93969262,0.42261826,-0.90630779),
line(0.42261826,-0.90630779,0.5,-0.8660254),
line(0.5,-0.8660254,0.57357644,-0.81915204),
line(0.57357644,-0.81915204,0.64278761,-0.76604444),
line(0.64278761,-0.76604444,0.70710678,-0.70710678),
line(0.70710678,-0.70710678,0.76604444,-0.64278761),
line(0.76604444,-0.64278761,0.81915204,-0.57357644),
line(0.81915204,-0.57357644,0.8660254,-0.5),
line(0.8660254,-0.5,0.90630779,-0.42261826),
line(0.90630779,-0.42261826,0.93969262,-0.34202014),
line(0.93969262,-0.34202014,0.96592583,-0.25881905),
line(0.96592583,-0.25881905,0.98480775,-0.17364818),
line(0.98480775,-0.17364818,0.9961947,-0.087155743),
line(0.9961947,-0.087155743,1,0) )}}}

Edwin</pre>