Question 91

PQRS is a cyclic quadrilateral and PQ is the diameter of the circle. If ∠RPQ = 38°, then what is the value (in degrees) of ∠PSR?

Solution

Given : PQRS is a cyclic quadrilateral and ∠RPQ = 38°

To find : ∠PSR = ?

Solution : PQ is the diameter, => $$\angle QRP=90^\circ$$ (Angle of the semi circle)

In $$\triangle$$ PQR,

=> ∠PQR + ∠QPR + QRP = 180°

=> ∠PQR + 90° + 38° = 180°

=> ∠PQR = 180° - 128° = 52°

Also, sum of opposite angles of a cyclic quadrilateral = 180°

=> ∠PQR + ∠PSR = 180°

=> ∠PSR = 180° - 52° = 128°

=> Ans - (C)

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