In triangle ABC, angle B = 70° and angle C = 50°. The bisectors of angle B and angle C meet at the point I. What is the measure of angle BIC?

The bisectors give angle IBC = 35° and angle ICB = 25°. In triangle BIC, angle BIC = 180° − 35° − 25° = 120°. This matches the standard result angle BIC = 90° + A/2 = 90° + 30° = 120°, since angle A = 60°.