Question

answer this question
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Answer 1

Answer:

AB || CE & AC is transversal ,

•°• angle BAC = angle ACE ( 1/2 angle ACD , since EC is bisector) { Alternate Interior Angle}

AB || CE & BE is transversal ,

•°• angle ABE = angle BEC ( Alternate Interior angle)

angle ABE = 1/2 angle ABC

Now,

angle ACD = angle ACE + angle ECD

angle ACD = 50° + 50° = 100°

angle ACD = angle BAC + angle ABC ( since angle ACD is exterior angle of triangle ABC and exterior angle of a triangle is equal to sum of two opposite interior angles )

angle ACD = 50° + 2 angle ABE ( since BE is bisector)

100° - 50° = 2 angle ABE

angle ABE = 50/2 = 25° or angle E = 25°