document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118697>Question 118697</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. If the measure of each of the interior angles of a regular polygon is 100 more than the measure of each of the exterior angles, name the polygon?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2.) Each of the measure of the interior and exterior angles of a regular polygon are in a ration 5:1.  Find the measure of an interior and an exterior angle and the name of the polygon.\r<BR>\n" );
document.write( "\n" );
document.write( "please help!\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86844 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=86844\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) You can use the following facts about polygons to help solve this problem:<BR>\n" );
document.write( "a) The sum of an interior angle and an exterior angle is 180 degrees.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bi%5D%2BA%5Be%5D+=+180 ALIGN=MIDDLE  ALT=\"A%5Bi%5D%2BA%5Be%5D+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b) The measure of an interior angle of a regular polygon of n sides is given by:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bi%5D+=+%28n-2%29180%2Fn ALIGN=MIDDLE  ALT=\"A%5Bi%5D+=+%28n-2%29180%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > This works only for \"regular\" polygons.<BR>\n" );
document.write( "In this problem, you have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bi%5D+=+A%5Be%5D%2B100 ALIGN=MIDDLE  ALT=\"A%5Bi%5D+=+A%5Be%5D%2B100\"   DISABLED_style= \"max-width:90%; height:auto;\" > \"The interior angle is 100 degrees more than the exterior angle\"<BR>\n" );
document.write( "So you can write:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bi%5D%2BA%5Be%5D+=+180 ALIGN=MIDDLE  ALT=\"A%5Bi%5D%2BA%5Be%5D+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bi%5D+=+A%5Be%5D%2B100 ALIGN=MIDDLE  ALT=\"A%5Bi%5D+=+A%5Be%5D%2B100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A%5Be%5D%2B100%29%2BA%5Be%5D+=+180 ALIGN=MIDDLE  ALT=\"%28A%5Be%5D%2B100%29%2BA%5Be%5D+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2A%5Be%5D%2B100+=+180 ALIGN=MIDDLE  ALT=\"2A%5Be%5D%2B100+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 100 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2A%5Be%5D+=+80 ALIGN=MIDDLE  ALT=\"2A%5Be%5D+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Be%5D+=+40 ALIGN=MIDDLE  ALT=\"A%5Be%5D+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" > The measure of an exterior angle is 40 degrees.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bi%5D+=+180-A%5Be%5D ALIGN=MIDDLE  ALT=\"A%5Bi%5D+=+180-A%5Be%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bi%5D+=+180-40 ALIGN=MIDDLE  ALT=\"A%5Bi%5D+=+180-40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bi%5D+=+140 ALIGN=MIDDLE  ALT=\"A%5Bi%5D+=+140\"   DISABLED_style= \"max-width:90%; height:auto;\" > The measure of an interior angle is 140 degrees.<BR>\n" );
document.write( "To find the number of sides (n) in this regular polygon, use:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bi%5D+=+%28n-2%29180%2Fn ALIGN=MIDDLE  ALT=\"A%5Bi%5D+=+%28n-2%29180%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bi%5D+=+140 ALIGN=MIDDLE  ALT=\"A%5Bi%5D+=+140\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=140+=+%28n-2%29180%2Fn ALIGN=MIDDLE  ALT=\"140+=+%28n-2%29180%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify and solve for n, the number of sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=140+=+%28180n-360%29%2Fn ALIGN=MIDDLE  ALT=\"140+=+%28180n-360%29%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by n.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=140n+=+180n-360 ALIGN=MIDDLE  ALT=\"140n+=+180n-360\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 360 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=140n%2B360+=+180n ALIGN=MIDDLE  ALT=\"140n%2B360+=+180n\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 140n from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360+=+40n ALIGN=MIDDLE  ALT=\"360+=+40n\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 40.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+=+n ALIGN=MIDDLE  ALT=\"9+=+n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The regular polygon has 9 sides and this is called a \"Nonagon\"\r<BR>\n" );
document.write( "\n" );
document.write( "2) In this problem, you have: \"The ratio of an interior angle to an exterior angle is 5:1 Or the interior angle is five times the exterior angle.<BR>\n" );
document.write( "Starting with: The sum of the interior and exterior angles is 180 degrees.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bi%5D%2BA%5Be%5D+=+180 ALIGN=MIDDLE  ALT=\"A%5Bi%5D%2BA%5Be%5D+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bi%5D+=+5%2AA%5Be%5D ALIGN=MIDDLE  ALT=\"A%5Bi%5D+=+5%2AA%5Be%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2AA%5Be%5D%2BA%5Be%5D+=+180 ALIGN=MIDDLE  ALT=\"5%2AA%5Be%5D%2BA%5Be%5D+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Be%5D ALIGN=MIDDLE  ALT=\"A%5Be%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2AA%5Be%5D+=+180 ALIGN=MIDDLE  ALT=\"6%2AA%5Be%5D+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 6.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Be%5D+=+30 ALIGN=MIDDLE  ALT=\"A%5Be%5D+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The exterior angle is 30 degrees.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bi%5D+=+180-A%5Be%5D ALIGN=MIDDLE  ALT=\"A%5Bi%5D+=+180-A%5Be%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Be%5D+=+30 ALIGN=MIDDLE  ALT=\"A%5Be%5D+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bi%5D+=+180-30 ALIGN=MIDDLE  ALT=\"A%5Bi%5D+=+180-30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bi%5D+=+150 ALIGN=MIDDLE  ALT=\"A%5Bi%5D+=+150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The interior angle is 150 degrees.<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bi%5D%2FA%5Be%5D+=+5%2F1 ALIGN=MIDDLE  ALT=\"A%5Bi%5D%2FA%5Be%5D+=+5%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bi%5D+=+150 ALIGN=MIDDLE  ALT=\"A%5Bi%5D+=+150\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Be%5D+=+30 ALIGN=MIDDLE  ALT=\"A%5Be%5D+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%2F30+=+5%2F1 ALIGN=MIDDLE  ALT=\"150%2F30+=+5%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce the fraction on the left side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F1+=+5%2F1 ALIGN=MIDDLE  ALT=\"5%2F1+=+5%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To find the number of sides (n), use:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bi%5D+=+%28n-2%29180%2Fn ALIGN=MIDDLE  ALT=\"A%5Bi%5D+=+%28n-2%29180%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bi%5D+=+150 ALIGN=MIDDLE  ALT=\"A%5Bi%5D+=+150\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150+=+%28n-2%29180%2Fn ALIGN=MIDDLE  ALT=\"150+=+%28n-2%29180%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify and solve for n. Multiply both sides by n.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150n+=+180n-360 ALIGN=MIDDLE  ALT=\"150n+=+180n-360\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 360 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150n%2B360+=+180n ALIGN=MIDDLE  ALT=\"150n%2B360+=+180n\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 150n from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360+=+30n ALIGN=MIDDLE  ALT=\"360+=+30n\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 30.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+=+n ALIGN=MIDDLE  ALT=\"12+=+n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This regular polygon has 12 sides and is called a \"Dodecagon\"\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );