document.write( "Question 162277: What is the size of each interior angle of a regular polygon if the number of sides is 4? 5? 6? 7? 8? 9? \n" ); document.write( "

Algebra.Com's Answer #119592 by Alan3354(69443) $\"\"$ $\"About$

You can put this solution on YOUR website!
What is the size of each interior angle of a regular polygon if the number of sides is 4? 5? 6? 7? 8? 9?
\n" ); document.write( "-------------------
\n" ); document.write( "The number of sides is the same as the number of angles and vertices.
\n" ); document.write( "The total of the interior angles of a polygon is 180*(n-2), where n is the number of sides, angles and vertices.
\n" ); document.write( "For regular polygons, all angles are equal, so they're the total/n.
\n" ); document.write( "That is 180*(n-2)/n
\n" ); document.write( "Just sub the number for n:
\n" ); document.write( "For 4, it's 360/4 = 90 degs
\n" ); document.write( "For 5, it's 540/5 = 108 degs
\n" ); document.write( "-------------
\n" ); document.write( "For 9, it's 1260/9 = 140 degs
\n" ); document.write( "For 36, it's 6120/36 = 170 degs
\n" ); document.write( "Notice that the angle increase as the number of sides increase. You can use that as a check for polygons with 5, 6, 7 & 8 sides.
\n" ); document.write( "---------
\n" ); document.write( "For 1000, it's 179.64 degs
\n" ); document.write( "As n approaches infinity (which is a circle), the angle approaches 180 degs.
\n" ); document.write( " \n" ); document.write( "

\n" );