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Angle between the bisector and the altitude from one vertex: half the difference of the other two angles

This type of question, asked 2 times: 15 Nov 2020 Tier II, 29 Jan 2022 Tier II. All 2 questions below, oldest first.

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  1. Question 1

    15 Nov 2020 Tier II

    15
    In Δ\DeltaPQR, ∠Q=84∘\angle Q = 84^\circ, ∠R=48∘\angle R = 48^\circ, PS ⊥\perp QR at S and the bisector of ∠P\angle P meets QR at T. What is the measure of ∠SPT\angle SPT?

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  2. Question 2

    29 Jan 2022 Tier II

    65
    In ΔABC\Delta ABC, ∠B=78∘\angle B = 78^\circ, ADAD is a bisector of ∠A\angle A meeting BCBC at DD, and AE⊥BCAE \perp BC at EE. If ∠DAE=24∘\angle DAE = 24^\circ, then the measure of ∠ACB\angle ACB is:

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