document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1031172>Question 1031172</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the measure of angles of a regular pentagon , (x-5), (x-6), (2x-7) ,x and(2x-2). find the value of x? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #645905 by </B><A HREF=/tutors/aboutme.mpl?userid=Bakr.R><B>Bakr.R(8)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Bakr.R><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/cgi-bin/show-face.mpl?user=Bakr.R><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=645905\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The question mentions the angles of a regular pentagon, with that information, we may assume that this polygon, or pentagon rather, has the properties of a regular polygon which means all sides are equal, and all angles are equal (meaning that they are the exact same).\r<BR>\n" );
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document.write( "The sides are irrelevant, being unknown they may be infinite, and the question does not require you to find them, so ignore that, and focus on the angles.\r<BR>\n" );
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document.write( "They give us five values, which are the values of the angles in the pentagon, and we know the sum interior angles (the total of the angles inside the shape), is equal to 540° (http://www.mathsisfun.com/geometry/interior-angles-polygons.html), and so, we can equal all the measurements in the question to 540. Let's start with a regular polygon:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Bakr.R&illustration_name=regular_pentagon\">. Now, let's fill out the information into the polygon: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Bakr.R&illustration_name=Numbered_pentagon\"> <BR>\n" );
document.write( "Keep in mind, that it is NOT definite that x is equal to 108 since its an angle on its own, this diagram is just to make the method simpler, and the question did not state that each value belongs in each separate angle.\r<BR>\n" );
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document.write( "Now, we may deduce the equation: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%2B%28x-6%29%2B%282x-7%29%2Bx%2B%282x-2%29=540 ALIGN=MIDDLE  ALT=\"%28x-5%29%2B%28x-6%29%2B%282x-7%29%2Bx%2B%282x-2%29=540\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Let's simplify the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x-20=540 ALIGN=MIDDLE  ALT=\"7x-20=540\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now, we are able to solve for x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x=560 ALIGN=MIDDLE  ALT=\"7x=560\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=560%2F70=80%B0 ALIGN=MIDDLE  ALT=\"x=560%2F70=80%B0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And so, the answer is x=80°, and degrees is for using the right unit of measure, since x is in the measurement of angles, don't forget that, or the answer may be marked as incorrect, but hopefully it wouldn't cause much of a problem.<BR>\n" );
document.write( "Good luck! </SPAN>\n" );
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