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.
2 answers:
Answer:
ADE = 34°
Step-by-step 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°
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