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 ?
Answer & explanation
Correct answer: option 3
∠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°