Question

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.

Answer 1

∠BEC = 34°

Step-by-step explanation:

In ∆ABC, By exterior angle theorem,

∠ACD = ∠A + ∠B

∠ACD = 68° + ∠B

½ ∠ACD = ½(68° + ∠B)

1/2∠ACD = 34° + 1/2∠B

34° = ½ ∠ ACD - ∠ EBC……. (1)

Now,

In ∆BEC, By exterior angle theorem,

∠ECD = ∠EBC + ∠E

∠E = ∠ECD - ∠EBC

∠E = 1/2∠ACD - ∠EBC …….(2)

From eq (1) and (2), we get

∠E = 34°i.e, ∠BEC = 34°

Hence, ∠BEC = 34°

Hope this answer will help you…..

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Answer 2

In ∆ABC,

∠ACD = ∠A + ∠B [By exterior angle theorem]

∠ACD = 68° + ∠B

½ ∠ACD = ½(68° + ∠B)

1/2∠ACD = 34° + 1/2∠B

34° = ½ ∠ ACD - ∠ EBC……. (i)

Again,

In ∆BEC

∠ECD = ∠EBC + ∠E [ By exterior angle theorem]

∠E = ∠ECD - ∠EBC

∠E = 1/2∠ACD - ∠EBC …….(ii)

From eq (i) and (i), we get

∠BEC = 34°