SOLUTION: 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 &

Algebra ->  Triangles -> SOLUTION: 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 &      Log On


   

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.
Answer by ikleyn(52788) About Me  (Show Source):
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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%28cross%28with%29%29 34° smaller than m∠CAB, find the measures of the angles of ΔADE.
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1.  Make a sketch.


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

    See the lesson Parallel lines 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°.

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