In ΔABC, AD and BE are the angle bisectors of ∠A and ∠B and DE ║ AB . If ∠ADE is with 34° smaller than ∠CAB, find the measures of the angles of ΔADE.
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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 ADE
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In ΔABC, AD and BE are the angle bisectors of ∠A and ∠B and DE║AB .
If m∠ADE is 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°.
.
In ΔABC, AD and BE are the angle bisectors of ∠A and ∠B and DE║AB .
If m∠ADE is 34° smaller than m∠CAB, find the measures of the angles of ΔADE.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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°.
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Answer:
Answer. in the triangle ADE angle EAD is
34°; angle EDA is 34°; angle AED is 180° -
34° - 34° = 102°.
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