document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=825165>Question 825165</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a regular polygon, the ratio of the measure of an exterior angle to the measure of an interior angle is 2:13. How many sides does the polygon have?\r<BR>\n" );
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document.write( "Thanks in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497083 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=497083\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An exterior and and interior angle of a polygon form a linear pair. This makes them are supplementary. So if<BR>\n" );
document.write( "x = the smaller angle, then<BR>\n" );
document.write( "180 - x =  the larger angle<br><BR>\n" );
document.write( "Then, since the ratio of these is 2:13:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28180-x%29+=+2%2F13 ALIGN=MIDDLE  ALT=\"x%2F%28180-x%29+=+2%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This can be solved. Cross-multiplying we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2A13+=+%28180-x%292 ALIGN=MIDDLE  ALT=\"x%2A13+=+%28180-x%292\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13x+=+360-2x ALIGN=MIDDLE  ALT=\"13x+=+360-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Adding 2x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x+=+360 ALIGN=MIDDLE  ALT=\"15x+=+360\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Dividing by 15:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+24 ALIGN=MIDDLE  ALT=\"x+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the exterior angle. Since the exterior angles add up to 360 and since they are all the same in a regular polygon, the number of exterior angles is:<BR>\n" );
document.write( "360/24 = 15.<BR>\n" );
document.write( "So the polygon has 15 exterior angles. And since the number of sides is the same as the number of exterior angles, the polygon has 15 sides, a 15-gon. </SPAN>\n" );
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