- A58°
- B32°
- C64°
- D116°
Step-by-Step Solution
∠ACD = ∠A + ∠B, so ½∠ACD = ½∠A + ½∠B. In △EBC, ∠ECD is exterior: ∠ECD = ∠BEC + ½∠B. Hence ∠BEC = ½∠ACD − ½∠B = ½∠A = 32°.
Answer: B) 32°
In △ABC, ∠A = 64°. The bisector of ∠ABC and the bisector of the exterior angle ∠ACD meet at E. Find ∠BEC.
Class 9Exterior Angle of a TriangleGeometry — Lines and Angles
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