document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=285063>Question 285063</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a regular polygon,the measure of each angle is 174*<BR>\n" );
document.write( "a)How many sides does the polygon have?<BR>\n" );
document.write( "b)How many diagonals does it have?<BR>\n" );
document.write( "c)What is the measure of an exterior angle?<BR>\n" );
document.write( "d)What is the sum of the measure of the interior angles? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #206709 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=206709\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a regular polygon,the measure of each angle is 174*<BR>\n" );
document.write( "Note: Each exterior angle is the supplement of an interior angle.<BR>\n" );
document.write( "So on your problem each exterior angle is 180-174 = 6 degrees<BR>\n" );
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document.write( "a)How many sides does the polygon have?<BR>\n" );
document.write( "Note: The sum of all of the exterior angles is 360 degrees.<BR>\n" );
document.write( "Since 360/6 = 60, the polygon has 60 exterior angles; so the<BR>\n" );
document.write( "polygon has 60 sides.<BR>\n" );
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document.write( "b)How many diagonals does it have?<BR>\n" );
document.write( "If it has 60 sides it has 60 vertices.<BR>\n" );
document.write( "The number of lines determined by those 60 vertices is<BR>\n" );
document.write( "60C2 = (60*59)/(1*2) = 1770<BR>\n" );
document.write( "60 of those lines are sides of the polygon.<BR>\n" );
document.write( "Therefore the polygon has 1770-60 = 1710 diagonals.<BR>\n" );
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document.write( "c)What is the measure of an exterior angle?<BR>\n" );
document.write( "6 degrees, as noted above<BR>\n" );
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document.write( "d)What is the sum of the measure of the interior angles?<BR>\n" );
document.write( "60*174 = 10440 degrees<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );