Q13 of 69 Page 9

In Fig. 9.42, side BC of Δ ABC is produced to point D such that bisectors of ∠ABC and ∠ACD meet at a point E. If ∠BAC = 68°, find ∠BEC.

By exterior angle theorem,

∠ACD = ∠A + ∠B


∠ACD = 68o + ∠B


∠ACD = 34o + ∠B


34o = ∠ACD - ∠EBC (i)


Now,


In


∠ECD = ∠EBC + ∠E


∠E = ∠ECD - ∠EBC


∠E = ∠ACD - ∠EBC (ii)


From (i) and (ii), we get


∠E = 34o


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