document.write( "Question 1009696: A parallelogram whose vertices are A(4,1),B(1,2), C(-5,-1)and D(-2,-2).find the angles of the vertices of the parallelogram. \n" ); document.write( "
Algebra.Com's Answer #625257 by Edwin McCravy(20054)\"\" \"About 
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document.write( "We find the slope of AB using the slope formula:\r\n" );
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document.write( "\"m\"\"%22%22=%22%22\"\"%28%282%29-%281%29%29%2F%28%281%29-%284%29%29\"\"%22%22=%22%22\"\"1%2F%28-3%29\"\"%22%22=%22%22\"\"-1%2F3\"\r\n" );
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document.write( "We find the slope of AD using the slope formula:\r\n" );
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document.write( "\"m\"\"%22%22=%22%22\"\"%28%28-2%29-%281%29%29%2F%28%28-2%29-%284%29%29\"\"%22%22=%22%22\"\"%28-3%29%2F%28-6%29\"\"%22%22=%22%22\"\"1%2F2\"\r\n" );
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document.write( "Then we use the formula for the tangent of the angle between two lines\r\n" );
document.write( "AB and AD:\r\n" );
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document.write( "\"tan%28theta%29\"\"%22%22=%22%22\"\"%28m%5B1%5D-m%5B2%5D%29%2F%281%2Bm%5B1%5Dm%5B2%5D%29\"\r\n" );
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document.write( "\"tan%28theta%29\"\"%22%22=%22%22\"\"%28+%28-1%2F3%29-%281%2F2%29+%29%2F%28+1%2B%28-1%2F3%29%281%2F2%29+%29\"\r\n" );
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document.write( "\"tan%28theta%29\"\"%22%22=%22%22\"\"%28+%28-1%2F3%29-%281%2F2%29+%29%2F%281-1%2F6%29\"\r\n" );
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document.write( "Multiply every term in the top and bottom by LCD=6\r\n" );
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document.write( "\"tan%28theta%29\"\"%22%22=%22%22\"\"%28+%28-1%2F3%29%2A6-%281%2F2%29%2A6+%29%2F%28+1%2A6-expr%281%2F6%29%2A6+%29\"\r\n" );
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document.write( "\"tan%28theta%29\"\"%22%22=%22%22\"\"%28-2-3%29%2F%286-1%29\"\r\n" );
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document.write( "\"tan%28theta%29\"\"%22%22=%22%22\"\"%28-5%29%2F5\"\r\n" );
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document.write( "\"tan%28theta%29\"\"%22%22=%22%22\"\"-1\"\r\n" );
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document.write( "This formula will give either the tangent of the acute or obtuse angle\r\n" );
document.write( "between two lines, which are supplementary, depending on our choice for\r\n" );
document.write( "m1 and m2.  The tangents of the acute and obtuse angles between two lines\r\n" );
document.write( "are different only by their signs.\r\n" );
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document.write( "Since A is acute, tan(A) = 1 and m∠A = 45°\r\n" );
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document.write( "Since the opposite interior angles of a parallelogram are equal in measure,\r\n" );
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document.write( "m∠C = 45°\r\n" );
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document.write( "Since adjacent interior angles of a parallelogram are supplementary,\r\n" );
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document.write( "m∠B = 180°-45° = 135° and since ∠D is opposite ∠B, m∠D also = 135°.\r\n" );
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document.write( "Edwin
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