document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148651>Question 148651</A>: <I><SPAN STYLE=\"word-break: break-all;\"> AH! I need help!\r<BR>\n" );
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document.write( "In the convex quadrilateral ABCD if ,angel a is congruent to angel d  and, measure of angel b=110 degrees and measure of c=60  find a .\r<BR>\n" );
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document.write( " a.95 ° <BR>\n" );
document.write( " b.170° <BR>\n" );
document.write( " c.190° <BR>\n" );
document.write( " d.360° \r<BR>\n" );
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document.write( " Suppose that the interior angles of a convex pentagon are five consecutive numbers. What is the measure of the largest angle?\r<BR>\n" );
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document.write( " a.105° <BR>\n" );
document.write( " b.106° <BR>\n" );
document.write( " c.109° <BR>\n" );
document.write( " d.110° \r<BR>\n" );
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document.write( " If the exterior angles of a convex octagon are , and  , calculate the smallest of the eight angles.\r<BR>\n" );
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document.write( " a.19° <BR>\n" );
document.write( " b.21° <BR>\n" );
document.write( " c.32° <BR>\n" );
document.write( " d.37° \r<BR>\n" );
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document.write( "If five of the exterior angles of a convex hexagon measure 55°, 60°, 63°, 70°, and 81°, find the measure of the sixth exterior angle.\r<BR>\n" );
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document.write( " a.31° <BR>\n" );
document.write( " b.60° <BR>\n" );
document.write( " c.120° <BR>\n" );
document.write( " d.391° \r<BR>\n" );
document.write( "\n" );
document.write( " If the exterior angles of a convex octagon are , and  , calculate the smallest of the eight angles.\r<BR>\n" );
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document.write( " a.19° <BR>\n" );
document.write( " b.21° <BR>\n" );
document.write( " c.32° <BR>\n" );
document.write( " d.37° \r<BR>\n" );
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document.write( " How many sides would a regular polygon have if each interior angle measures 162°?\r<BR>\n" );
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document.write( " a.10 <BR>\n" );
document.write( " b.12 <BR>\n" );
document.write( " c.18 <BR>\n" );
document.write( " d.20 \r<BR>\n" );
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document.write( "How many angles would a regular polygon have if each exterior angle measures 5°?\r<BR>\n" );
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document.write( " a.36 <BR>\n" );
document.write( " b.37 <BR>\n" );
document.write( " c.72 <BR>\n" );
document.write( " d.74 \r<BR>\n" );
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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 #109088 by </B><A HREF=/tutors/aboutme.mpl?userid=mangopeeler07><B>mangopeeler07(462)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mangopeeler07><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=109088\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. In the convex quadrilateral ABCD if ,angel a is congruent to angel d  and, measure of angel b=110 degrees and measure of c=60  find a .\r<BR>\n" );
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document.write( " a.95 ° <BR>\n" );
document.write( " b.170° <BR>\n" );
document.write( " c.190° <BR>\n" );
document.write( " d.360° \r<BR>\n" );
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document.write( "add b and c: 110 +60=170<BR>\n" );
document.write( "subtract that from 360, since the degrees of a quad is 360:<BR>\n" );
document.write( "360-170=190<BR>\n" );
document.write( "Divide that by two since a and d are congruent<BR>\n" );
document.write( "190/2=95\r<BR>\n" );
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document.write( "So the answer is a)95 degrees.<BR>\n" );
document.write( "________________________________________________________________________________<BR>\n" );
document.write( "2. Suppose that the interior angles of a convex pentagon are five consecutive numbers. What is the measure of the largest angle?\r<BR>\n" );
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document.write( " a.105° <BR>\n" );
document.write( " b.106° <BR>\n" );
document.write( " c.109° <BR>\n" );
document.write( " d.110° \r<BR>\n" );
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document.write( "Since these five numbers are consecutive, then this can be written as:<BR>\n" );
document.write( "x+(x+1)+(x+2)+(x+3)+(x+4)<BR>\n" );
document.write( "Set that equal to 540, since the angles of pentagon add up to 540:<BR>\n" );
document.write( "x+(x+1)+(x+2)+(x+3)+(x+4)=540<BR>\n" );
document.write( "Combine like terms:<BR>\n" );
document.write( "5x+10=540<BR>\n" );
document.write( "5x=530<BR>\n" );
document.write( "x=106\r<BR>\n" );
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document.write( "Largest angle=x+4 or 106+4<BR>\n" );
document.write( "Largest angle=110 degrees\r<BR>\n" );
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document.write( "So the answer is d)110 degrees.<BR>\n" );
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document.write( "3. If five of the exterior angles of a convex hexagon measure 55°, 60°, 63°, 70°, and 81°, find the measure of the sixth exterior angle.\r<BR>\n" );
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document.write( " a.31° <BR>\n" );
document.write( " b.60° <BR>\n" );
document.write( " c.120° <BR>\n" );
document.write( " d.391° \r<BR>\n" );
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document.write( "First find the measure of the first five interior angles, which can be found by subtracting the exterior angle from 180.  You get:<BR>\n" );
document.write( "125, 120, 117, 110, and 99.<BR>\n" );
document.write( "Now add them together:<BR>\n" );
document.write( "125+120+117+110+99=571<BR>\n" );
document.write( "Now subtract that from 720, since the degrees of a hexagon add up to 720.<BR>\n" );
document.write( "720-571=149<BR>\n" );
document.write( "That is the sixth interior angle.  Now subtract that from 180 to get the exterior:<BR>\n" );
document.write( "180-149=31\r<BR>\n" );
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document.write( "So the answer is a)31 degrees.<BR>\n" );
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document.write( "4.  How many sides would a regular polygon have if each interior angle measures 162°?\r<BR>\n" );
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document.write( " a.10 <BR>\n" );
document.write( " b.12 <BR>\n" );
document.write( " c.18 <BR>\n" );
document.write( " d.20\r<BR>\n" );
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document.write( "Use the formula [180(n-2)]/n to get the measure of an interior angle of a regular polygon.  If each angle is 162, then set it equal to that:\r<BR>\n" );
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document.write( "[180(n-2)]/n=162<BR>\n" );
document.write( "Now multiply both sides by n<BR>\n" );
document.write( "180(n-2)=162n\r<BR>\n" );
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document.write( "Distribute 180 to n-2<BR>\n" );
document.write( "180n-360=162n<BR>\n" );
document.write( "Subtract 180n from both sides<BR>\n" );
document.write( "-360=-18n<BR>\n" );
document.write( "Divide both sides by -18<BR>\n" );
document.write( "20=n\r<BR>\n" );
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document.write( "So the answer is d)20 sides.<BR>\n" );
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document.write( "5. How many angles would a regular polygon have if each exterior angle measures 5°?\r<BR>\n" );
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document.write( " a.36 <BR>\n" );
document.write( " b.37 <BR>\n" );
document.write( " c.72 <BR>\n" );
document.write( " d.74 \r<BR>\n" );
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document.write( "First get the measure of the interiors by subtracting the exterior from 180:<BR>\n" );
document.write( "180-5=175.<BR>\n" );
document.write( "Then use [180(n-2)]/n as in the last question, but this time set it equal to 175:\r<BR>\n" );
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document.write( "[180(n-2)]/n=175\r<BR>\n" );
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document.write( "Now multiply both sides by n<BR>\n" );
document.write( "180(n-2)=175n\r<BR>\n" );
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document.write( "Distribute 180 to n-2<BR>\n" );
document.write( "180n-360=175n<BR>\n" );
document.write( "Subtract 180n from both sides<BR>\n" );
document.write( "-360=-5n<BR>\n" );
document.write( "Divide both sides by -5<BR>\n" );
document.write( "72=n\r<BR>\n" );
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document.write( "So the answer is c)72 angles. </SPAN>\n" );
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