Question

In ΔABC, the internal bisectors of ∠ABC and ∠ACB met at I and ∠BAC = 50°. The measure of ∠BIC is

Answer 1

∠BIC = 90° + 1/2 ∠BAC
= 90° + 1/2 × 50 = 115°

Answer 2

Answer:

115°

Step-by-step explanation:

In ∆ABC

∠ABC + ∠ACB = 180° - 50° = 130°

In ∆BIC

Two angles are half of ∠ABC and ∠ACB, therefore their sum will be half of sum of angles.

∠IBC + ∠ICB = 130/2 = 65°

∠BIC = 180° - 65° = 115°