document.write( "Question 1154687: If DE and BC are parallel, angle 3 = angle 4 = 2(angle 2) and angle 6 = angle 2 + 12 degrees, find the measure of angle 1.\r
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Algebra.Com's Answer #777159 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "given:\r
\n" ); document.write( "\n" ); document.write( " $\"DE\"$ and $\"BC\"$ are parallel, \r
\n" ); document.write( "\n" ); document.write( " < $\"3\"$ = < $\"4\"$ = $\"2\"$ *< $\"2\"$ \r
\n" ); document.write( "\n" ); document.write( " from the graph we see that\r
\n" ); document.write( "\n" ); document.write( "< $\"+1\"$ = < $\"5\"$ + < $\"6+\"$ as corresponding angles \r
\n" ); document.write( "\n" ); document.write( "< $\"5\"$ = < $\"2\"$ as alternate interior angles\r
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\n" ); document.write( "\n" ); document.write( "if < $\"3\"$ = < $\"4\"$ = $\"2\"$ *< $\"2\"$ , < $\"5\"$ = < $\"2\"$ , and if < $\"2\"$ is $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( "their sum is
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< $\"2\"$ = $\"36\"$ ° and $\"m\"$ < $\"5\"$ = $\"36\"$ °\r
\n" ); document.write( "\n" ); document.write( " $\"m\"$ < $\"3\"$ = $\"m\"$ < $\"4\"$ = $\"2\"$ *< $\"36\"$ = $\"72\"$ °\r
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\n" ); document.write( "\n" ); document.write( "and if $\"m\"$ < $\"+6\"$ = < $\"2\"$ + $\"12\"$ ° , we have
\n" ); document.write( " $\"m\"$ < $\"+6\"$ = $\"12%2B36\"$ = $\"48\"$ °\r
\n" ); document.write( "\n" ); document.write( " $\"m\"$ < $\"DEB\"$ = $\"180-%2848%2B36%29=96\"$ °\r
\n" ); document.write( "\n" ); document.write( " $\"m\"$ < $\"+1\"$ = $\"36%2B48\"$ °= $\"84\"$ °\r
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\n" ); document.write( "\n" ); document.write( "so, $\"m\"$ < $\"+1\"$ = $\"84\"$ °\r
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\n" ); document.write( "\n" ); document.write( "check if the sum of $\"m\"$ < $\"DEB%7D%7D+and+%7B%7B%7Bm\"$ < $\"+1\"$ is $\"180\"$ °\r
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\n" ); document.write( "\n" ); document.write( " $\"m\"$ < $\"DEB%7D%7D+%2B+%7B%7B%7Bm\"$ < $\"+1\"$ = $\"96%2B84\"$ °= $\"180\"$ °\r
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