Question

3. In Fig. 9.42, side BC of AABC is produced to point D such that bisectors of
ZABC and ZACD meet at a point E. If ZBAC = 68°, find ZBEC.​

Answer 1

Answer:

∠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°

∠BEC = 34°

Hence, ∠BEC = 34°