Question 62

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 $$\angle BEC$$?

Solution

In $$\triangle ABC$$,

$$\angle A + \angle B + \angle C = 180\degree$$

$$\angle A = 180 - 72 - 44 = 64\degree$$

By angle bisector property,

$$\angle BEC = \frac{\angle A}{2}$$

$$\angle BEC = \frac{64\degree}{2} = 32\degree$$

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