The point of intersection of the diagonals PR and QS of the cyclic quadrilateral PQRS is A. If ∠PAQ = 64° and ∠RQS = 28°, then the measure of ∠PSQ is ?

36°

∠PAQ + ∠RAQ = 180°

64° + ∠RAQ = 180°

        ∠RAQ = 116°

In ΔARQ

∠RAQ + ∠AQR + ∠ARQ = 180°

116° + 28° + ∠ARQ = 180°

                   ∠ARQ = 180° - (144°)

                  ∠ARQ = 36°

∠PRQ = ∠PSQ      [∴ angle made by same chord on circumference are same]

⇒  ∠PSQ = 36°