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In the figure (i) given below, PQRS is a cyclic quadrilateral in which PQ = QR and RS is produced to T. If ∠QPR = 52°, calculate ∠PST.

In the figure (i) given below, PQRS is a cyclic quadrilateral in which PQ = QR and RS is produced to T. If ∠QPR = 52°, calculate ∠PST. Circles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

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Answer

Given, ∠QPR = 52°.

Since PQ = PR so, ∠QRP = ∠QPR = 52°.

Since sum of angles of triangle = 180°

In △PQR

⇒ ∠QPR + ∠QRP + ∠PQR = 180°
⇒ 52° + 52° + ∠PQR = 180°
⇒ 104° + ∠PQR = 180°
⇒ ∠PQR = 180° - 104°
⇒ ∠PQR = 76°.

∵ exterior angle of a cyclic quadrilateral is equal to the opposite interior angle.

∠PST = ∠PQR = 76°

Hence, the value of ∠PST = 76°

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