PQRS is a cyclic quadrilateral. If \(\angle P\) is twice \(\angle R\) and \(\angle S\) is four times \(\angle Q\), what is the sum of \(\angle Q\) and \(\angle R\)?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 96°
In a cyclic quadrilateral the opposite angles add up to \(180^\circ\): \(\angle P+\angle R=180^\circ\) and \(\angle Q+\angle S=180^\circ\).
\(2\angle R+\angle R=180^\circ\), so \(\angle R=60^\circ\)
\(\angle Q+4\angle Q=180^\circ\), so \(\angle Q=36^\circ\)
\(\angle Q+\angle R=36^\circ+60^\circ=96^\circ\)