Question

In ∆ ABC , AB=AC and Bisector of angle B and angle C intersect at l . If angle BCA =70° , then angle BAI is equal to​

Answer 1

Since the angles opposite to equal sides are equal,

∴AB=AC

⇒∠C=∠B

⇒

2

∠B

=

2

∠C

.

Since BO and CO are bisectors of ∠B and ∠C, we also have

∠ABO=

2

∠B

and ∠ACO=

2

∠C

.

∠ABO=

2

∠B

=

2

∠C

=∠ACO.

Consider △BCO:

∠OBC=∠OCB

⇒BO=CO .. [Sides opposite to equal angles are equal]

Finally, consider triangles ABO and ACO.

BA=CA.. (given);

BO=CO .. (proved);

∠ABO=∠ACO (proved).

Hence, by S.A.S postulate

△ABO≅△ACO

⇒∠BAO=∠CAO⇒AO bisects ∠A.