Question

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

ADE = 34°

Explanation:

To solve a question in which a shape is described, the first step must be to draw a diagram based on the information provided. Based on the information provided in a diagrammatic form, it can be seen clearly that lines DE and BA are parallel. Therefore, angle ADE and DAB are equal. It is also mentioned that line AD is the bisector of angle CAB. From the information provided, below correlations are determined.

CAB - 34 = ADE

ADE = DAB

DAB = DAC

CAB = DAB + DAC

This gives:

CAB = 2xDAB = 2xADE

When the above equations are reduced,

CAB - 34 = ADE

2xADE - 34 = ADE

ADE = 34°