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 1

Draw and label a diagram!

Include the following:

m∠BAD = m∠ADE by alternate interior angles

∠mABE = m∠BED by alternate interior angles

Now use the congruent triangles. to solve and answer.

Answer 2

∠ADE = ∠CAB -34

∠ADE = (1/) of ∠CAB because of alternate interior angles of parallel lines

(1/2)∠CAB = ∠CAB - 34 => ∠CAB = 68° and ∠ADE = 34°