Question
PQRS is a cyclic trapezium where PQ is parallel to RS
and PQ is the diameter. If ∠QPR = 40° then the ∠PSR is equal to:Solution
Angle made in a semicircle is a right angle. The sum of the opposite angles of a cyclic trapezium is 180°. In triangle PQR, ∠RPQ + ∠RQP + ∠QRP = 180° [Angle sum property] ⇒ 40° + ∠RQP + 90° = 180° ⇒ ∠RQP = 180° - 130° = 50° ∠RQP + ∠PSR = 180° [Supplementary Angles] ∴ ∠PSR = 180° - 50° = 130°
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