In triangle ABC, m∠BAC = 50°. If m∠ACB = 30°, then the triangle is triangle. If m∠ABC = 40°, then the triangle is triangle. If triangle ABC is isosceles, and AB = 6 and BC = 4, then AC = .

When ∠ACB is 30°, the third angle is 180° − 50° − 30° = 100°, so the triangle is obtuse. If ∠ABC is 40°, the third angle is 180° − 50° − 40° = 90°, so the triangle is right. For an isosceles triangle, AC must match one of the other sides; since AB = 6 and BC = 4, AC can be 4 or 6, which is choice C.

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