Question

Let D be an interior point of the side BC of a triangle ABC. Let I₁ and I₂ be the incentres of triangles ABD and ACD respectively. Let AI₁ and AI₂ meet BC in E and F respectively. If ∠BI₁ E = 60°, what is the measure of ∠CI₂F in degrees?

Answer 1

90° + 60° + θ = 180°

∴ θ = 30°