document.write( "Question 1162497: In triangle PQR, X is a point on QR such that angle RPX = angle Q. Prove that angle PXR = angle QPR \n" ); document.write( "
Algebra.Com's Answer #786348 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We are to prove that the angles with the green arcs are equal, \r\n" );
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document.write( "∠PXR = ∠QPR\r\n" );
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document.write( "given\r\n" );
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document.write( "that the angles with the red arcs are equal,\r\n" );
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document.write( "∠RPX = ∠Q\r\n" );
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document.write( "We use the fact that the three internal angles of a triangle have sum 180°,\r\n" );
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document.write( "For ΔPQR, \r\n" );
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document.write( "(1)  ∠QPR + ∠R + ∠Q = 180°. Therefore,\r\n" );
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document.write( "(2)  ∠QPR = 180° - ∠R - ∠Q\r\n" );
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document.write( "For ΔRPX, \r\n" );
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document.write( "(3)  ∠PXR + ∠R + ∠RPX = 180°. Therefore, \r\n" );
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document.write( "(4)  ∠PXR = 180° - ∠R - ∠RPX \r\n" );
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document.write( "Since we are given that ∠RPX = ∠Q, the right sides\r\n" );
document.write( "of (2) and (4) are equal, so their left sides are also equal. \r\n" );
document.write( "Therefore,\r\n" );
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document.write( "∠PXR = ∠QPR\r\n" );
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document.write( "Now you can write that up in a two-column proof.\r\n" );
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document.write( "Edwin

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