\(\square PQRS\) is a cyclic quadrilateral. If \(\angle P = (2x + 10)^\circ\) and \(\angle R = (x + 35)^\circ\), find x, \(\angle P\) and \(\angle R\).

Doubtly Asked 29 Oct 2026 Practice test ssc 10th Save WhatsApp Report

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Answer: x = 45, \(\angle P = 100^\circ\), \(\angle R = 80^\circ\)

Opposite angles of a cyclic quadrilateral are supplementary: \((2x + 10) + (x + 35) = 180\) \(\therefore 3x + 45 = 180\) \(\therefore x = 45\).

\(\angle P = 2(45) + 10 = 100^\circ\), \(\angle R = 45 + 35 = 80^\circ\). Check: \(100 + 80 = 180\).

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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