document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169678>Question 169678</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0866099654/algebrahomeworkh>Geometry for enjoyment and challegne</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The measure of one angle of a parallelogram is 40 more than 3 times another. Find the measure of each angle.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125089 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=125089\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> in a parallelogram, the opposite angles are equal to each other.<BR>\n" );
document.write( "the sum of the angles in a parallelogram is 360.<BR>\n" );
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document.write( "if the parallelogram is labeled ABCD, then angle A is equal to angle C because they are opposite each other, and angle B is equal to angle D because they are opposite to each other.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the labeling of the parallelogram would be:<BR>\n" );
document.write( "A is lower left corner<BR>\n" );
document.write( "B is upper left corner<BR>\n" );
document.write( "C is upper right corner<BR>\n" );
document.write( "D is lower right corner<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "assume A and C are the smaller angles.<BR>\n" );
document.write( "assume B and D are the larger angles.<BR>\n" );
document.write( "the parallelogram will be tilting to the right so that corner B is to the right of corner A.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "problem states that the larger angle is 3 times the smaller angle plus 40 degrees.<BR>\n" );
document.write( "since B is the larger angle and A is the smaller angle, that means that:<BR>\n" );
document.write( "B = 3*A + 40<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since the sum of the angles in a parallelogram = 360 degrees then angle A + B + C + D = 360.<BR>\n" );
document.write( "since angle A = angle C, and angle B = angle D, this can be rewritten as 2*A + 2*B = 360 degrees by substituting A for C and B for D.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "equation you start out with is:<BR>\n" );
document.write( "2*A + 2*B = 360<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you know that B = 3*A + 40 so you can substitute in equation.<BR>\n" );
document.write( "2*A + 2*B = 360 becomes:<BR>\n" );
document.write( "2*A + 2*(3*A+40) = 360<BR>\n" );
document.write( "simplify:<BR>\n" );
document.write( "2*A + 2*3*A + 2*40 = 360<BR>\n" );
document.write( "2*A + 6*A + 80 = 360<BR>\n" );
document.write( "8*A + 80 = 360<BR>\n" );
document.write( "subtract 80 from both sides of equation:<BR>\n" );
document.write( "8*A = 360 - 80<BR>\n" );
document.write( "8*A = 280<BR>\n" );
document.write( "divide both sides of equation by 8:<BR>\n" );
document.write( "A = 280 / 8<BR>\n" );
document.write( "A = 35<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "angle A is 35 degrees.<BR>\n" );
document.write( "angle B is 3 * 35 + 40<BR>\n" );
document.write( "angle B is 145 degrees.<BR>\n" );
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document.write( "angle A and angle B = 180 degrees.<BR>\n" );
document.write( "2 * angle A and 2 * angle B = 360 degrees.<BR>\n" );
document.write( "this checks out with the sum of the angles of a parallelogram so the angles are good.<BR>\n" );
document.write( "answer is:<BR>\n" );
document.write( "smaller angle is 35 degrees.<BR>\n" );
document.write( "larger angle is 145 degrees.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );