Question 1209478: In triangle ABC, DE is parallel to BC and AD = DE = BE.
If BE is the angle bisector of angle CBA, then find the measure of angle ACB.
Link to the graph: https://ibb.co/h9RJzZR
Answer by greenestamps(13200)   (Show Source):
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Since BE bisects angle CBA, let x be the measure of each of angles CBE and EBD.
In triangle DEB, DE = BE, so the measure of angle BDE is also x.
That makes the measure of angle EDA 180-x.
But DE and BC are parallel, so angles EDA and CBA are congruent.
2x = 180-x
3x = 180
x = 60
In triangle EDA, AD = DE, so angles DAE and DEA are congruent. Then, since the measure of angle EDA is 180-x=120, the measure of each of angles DAE and DEA is x/2 = 30.
And again DE and BC are parallel, so the measure of angle ACB is also 30.
ANSWER: 30 degrees
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