Задача 9 ∠B

Сумма углов треугольника равна 180°.

∠BAC + ∠ABC + ∠BCA = 180°

∠BCA = 180° - ∠BAC - ∠ABC = 180° - ∠BAC - ∠ABC

∠A = ∠C, так как AH и CK - биссектрисы.

∠AHB = ∠CKB = 110°

∠ABH = ∠BCK

Рассмотрим треугольник ΔBOC.

∠BOC + ∠OBC + ∠OCB = 180°

∠OBC + ∠OCB = 180° - ∠BOC = 180° - 110° = 70°

∠OBC = ∠ABC / 2

∠OCB = ∠BCA / 2

∠OBC + ∠OCB = ∠ABC / 2 + ∠BCA / 2 = 70°

∠ABC + ∠BCA = 2 * 70° = 140°

∠BAC + ∠ABC + ∠BCA = 180°

∠BAC = 180° - ∠ABC - ∠BCA = 180° - 140° = 40°

∠BAC = ∠BCA = 40°

∠ABC = 140° - ∠BCA = 140° - 40° = 100°

Ответ: ∠B = 100°