In $$\triangle ABC, \angle B = 72^\circ$$ and $$\angle C = 44^\circ$$. Side BC is produced to D. The bisectors of $$\angle B$$ and $$\angle ACD$$ meet at E. What is the measure of $$\angle BEC$$?
In $$\triangle ABC$$,
$$\angle A +Â \angle B +Â \angle C = 180\degree$$
$$\angle A = 180 - 72 - 44 = 64\degree$$
By angle bisector property,
$$\angle BEC = \frac{\angle A}{2}$$
$$\angle BEC = \frac{64\degree}{2} = 32\degree$$
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