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In triangle ABC, ∠B = 64° and ∠C = 36°. The internal bisector of ∠B meets the bisector of the exterior angle at C at the point E. Find ∠BEC.

Competition practiceGeometry

A40°
B50°
C80°
D140°

Step-by-Step Solution

∠

A = 180° - 64° - 36° = 80°

. The exterior angle at

C

is

∠ A + ∠ B

, so half of it equals half of ∠

B

plus ∠

BEC

, which gives

∠ BEC = \frac{∠ A}{2} = 40°

.

Answer: A) 40°

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