document.write( "Question 1197065: Find angle C, in degrees in the following Diagram:\r
\n" ); document.write( "\n" ); document.write( "Please find my diagram here: https://drive.google.com/file/d/1BkVlpWbTavh-X4fBbyDESblXowg0eNii/view?usp=sharing\r
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Algebra.Com's Answer #830210 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            The solution by @MathLover1 is INCORRECT.\r
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\n" ); document.write( "\n" ); document.write( "            It is incorrect, because she starts from wrong assumption that \" there are three right angled triangles \".\r
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\n" ); document.write( "\n" ); document.write( "            The problem NOWHERE says it: this assumption is not supported by the problem,\r
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document.write( "Let A be the vertex at angle \"a\";\r\n" );
document.write( "    B be the vertex at angle \"b\",\r\n" );
document.write( "    C be the vertex at angle \"c\",\r\n" );
document.write( "    D be the vertex at angle 37°,\r\n" );
document.write( "    P be the intersection point of the two sloped lines.\r\n" );
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document.write( "From triangle ABC, we can write equation \r\n" );
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document.write( "    angle(A) + angle(B)  + angle(C) = 180°\r\n" );
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document.write( "or\r\n" );
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document.write( "    2a       + (180°-2b) +    c     = 180°\r\n" );
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document.write( "or\r\n" );
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document.write( "    2a - 2b  + c =  0.     (1)\r\n" );
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document.write( "Next consider triangles APC and BPD.  From these triangles, we can write equation\r\n" );
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document.write( "    a + c = b + 37°.\r\n" );
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document.write( "It is because left  side (a+c) complements angle P to 180°,\r\n" );
document.write( "same as       right side (b+37°) complements angle P to 180°.\r\n" );
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document.write( "Last equation is equivalent to\r\n" );
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document.write( "    a - b + c = 37°.       (2)\r\n" );
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document.write( "Thus we have two equations (1) and (2)\r\n" );
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document.write( "    2a - 2b  + c =  0.     (1)\r\n" );
document.write( "    a  -  b  + c = 37°.    (2)\r\n" );
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document.write( "Multiply equation (2) by 2;  then subtract equation (1).  You will get\r\n" );
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document.write( "    c = 2*37° = 74°.\r\n" );
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document.write( "ANSWER.  The measure of angle \"c\" is 74°.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved (correctly).\r
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