Question
Download Solution PDFPQRS is a cyclic trapezium where PQ is parallel to SR and PQ is the diameter. If ∠QPR = 40° then the ∠PSR is equal to:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
PQRS is a cyclic trapezium where PQ is parallel to RS.
PQ is the diameter & ∠QPR = 40°
Concept:
Angle made in a semicircle is a right angle.
The sum of the opposite angles of a cyclic trapezium is 180°.
Calculation:
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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