document.write( "Question 1189508: In the diagram below, Angle DCE=Angle ACB, Angle BCF is a right angle, and CE ⊥ AB. Find the measure of Angle BAD\r
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Algebra.Com's Answer #820961 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Since ∠BCF is a right angle, ΔBCF is a right triangle and\r\n" );
document.write( "m∠FCG = 90o - 23o = 67o.\r\n" );
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document.write( "The fact that CE ⊥ AB, means that an extension of CE down to an \r\n" );
document.write( "extension of AB, the extensions will intersect at a right angle. So\r\n" );
document.write( "we extend EC down to FA, which is a left extension of AB. Let G be \r\n" );
document.write( "the point where the extension of EC intersepts FA.\r\n" );
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document.write( "Now that we extended EC to G we see that ∠DCE ≅ ∠ACG because\r\n" );
document.write( "they are vertical angles. We also see that \r\n" );
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document.write( "Since ∠CGF is a right angle, ΔCGF is a right triangle and\r\n" );
document.write( "m∠GCF = 90o - 67o = 23o.\r\n" );
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document.write( "Let the common measure of ∠DCE, ∠ACG, and ∠ACB be xo\r\n" );
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document.write( "Since Angle BCF is a right angle,\r\n" );
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document.write( "\"23%5Eo%2Bx%5Eo%2Bx%5Eo\"\"%22%22=%22%22\"\"90%5Eo\"\r\n" );
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document.write( "\"23%5Eo%2B2x%5Eo\"\"%22%22=%22%22\"\"90%5Eo\"\r\n" );
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document.write( "\"2x%5Eo\"\"%22%22=%22%22\"\"67%5Eo\"\r\n" );
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document.write( "\"x%5Eo\"\"%22%22=%22%22\"\"33.5%5Eo\"\r\n" );
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document.write( "Since the three angles of ΔBAC must have sum 180o,\r\n" );
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document.write( "m∠BAD + m∠ABC + m∠BCA = 180o\r\n" );
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document.write( "m∠BAD + 23o + 33.5o = 180o\r\n" );
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document.write( "m∠BAD + 56.5o = 180o\r\n" );
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document.write( "m∠BAD = 123.5o\r\n" );
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document.write( "Edwin
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