document.write( "Question 1066810: In ΔABC, AD and BE are the angle bisectors of ∠A and ∠B and DE║AB . If m∠ADE is with 34° smaller than m∠CAB, find the measures of the angles of ΔADE. \n" ); document.write( "

Algebra.Com's Answer #682147 by ikleyn(52794) $\"\"$ $\"About$

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\n" ); document.write( "In ΔABC, AD and BE are the angle bisectors of ∠A and ∠B and DE║AB .
\n" ); document.write( "If m∠ADE is $\"highlight%28cross%28with%29%29\"$ 34° smaller than m∠CAB, find the measures of the angles of ΔADE.
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document.write( "1.  Make a sketch.\r\n" );
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document.write( "2.  The angle ADE is congruent to the angle DAB, since they are alternate interior angles.  \r\n" );
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document.write( "    See the lesson Parallel lines in this site.  \r\n" );
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document.write( "3.  Hence, the angle DAB is 34° smaller than the angle CAB.\r\n" );
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document.write( "4.  At the same time the angle DAB is half of the angle CAB.\r\n" );
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document.write( "    It implies that the measure of the angle CAB is 2*34° = 78°.\r\n" );
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document.write( "5.  In turn, it implies that in the triangle ADE\r\n" );
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document.write( "    angle EAD is 34°;  angle EDA is 34°;  angle AED is 180° - 34° - 34° = 102°.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. in the triangle ADE angle EAD is 34°; angle EDA is 34°; angle AED is 180° - 34° - 34° = 102°.\r
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