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Angle where two angle bisectors of a triangle meet (90 plus or minus A/2)

This type of question, asked 3 times: CDS 1 2017, CDS 2 2018, CDS 1 2025. All 3 questions below, oldest first.

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  1. Question 1

    CDS 1 2017

    94
    In the figure given below, ∠A=80∘\angle A = 80^\circ and ∠ABC=60∘\angle ABC = 60^\circ. BD and CD bisect angles B and C respectively. What are the values of x and y respectively ?

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  2. Question 2

    CDS 2 2018

    85
    In a triangle ABC, the sides AB, AC are produced and the bisectors of exterior angles of ∠ABC\angle ABC and ∠ACB\angle ACB intersect at D. If ∠BAC=50∘\angle BAC = 50^\circ, then ∠BDC\angle BDC is equal to

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  3. Question 3

    CDS 1 2025

    18
    The measure of an angle formed by the bisectors of the angles A and C of the triangle ABC is 130∘130^\circ. What is the measure of the angle B ?

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