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Opposite angles of a cyclic quadrilateral add to 180: find an angle or expression

This type of question, asked 3 times: CDS 2 2020, CDS 1 2022, CDS 2 2026. All 3 questions below, oldest first.

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  1. Question 1

    CDS 2 2020

    63
    ABCD is a cyclic quadrilateral. The bisectors of the angles A, B, C and D cut the circle at P, Q, R and S respectively. What is ∠PQR+∠RSP\angle PQR + \angle RSP equal to ?

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  2. Question 2

    CDS 1 2022

    52
    If AA, BB, CC, DD are the angles of a cyclic quadrilateral, then what is the value of the following? sin⁡(A+C2)+sin⁡(B+D2)\sin\left(\frac{A + C}{2}\right) + \sin\left(\frac{B + D}{2}\right)

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  3. Question 3

    CDS 2 2026

    51
    In a cyclic quadrilateral ABCD, ∠A=(4x+3)∘\angle A = (4x + 3)^\circ, ∠B=(3y+9)∘\angle B = (3y + 9)^\circ, ∠C=(4y−3)∘\angle C = (4y - 3)^\circ, ∠D=(5x−10)∘\angle D = (5x - 10)^\circ. What is ∠A+∠B\angle A + \angle B equal to ?

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