Question 1066810
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In ΔABC, AD and BE are the angle bisectors of ∠A and ∠B and DE║AB . 
If m∠ADE is {{{highlight(cross(with))}}} 34° smaller than m∠CAB, find the measures of the angles of ΔADE.
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<pre>
1.  Make a sketch.


2.  The angle ADE is congruent to the angle DAB, since they are <U>alternate interior angles</U>.  

    See the lesson <A HREF=https://www.algebra.com/algebra/homework/Angles/Parallel-lines.lesson>Parallel lines</A> in this site.  


3.  Hence, the angle DAB is 34° smaller than the angle CAB.


4.  At the same time the angle DAB is half of the angle CAB.

    It implies that the measure of the angle CAB is 2*34° = 78°.


5.  In turn, it implies that in the triangle ADE

    angle EAD is 34°;  angle EDA is 34°;  angle AED is 180° - 34° - 34° = 102°.
</pre>

<U>Answer</U>.  in the triangle  ADE  angle EAD is 34°;  angle EDA is 34°;  angle AED is 180° - 34° - 34° = 102°.