In quadrilateral PQRS, \(\angle P = 2\angle Q,\ \angle Q = \dfrac{\angle R}{4},\ \angle R = 2\angle S\). Find the value of \(\angle S\).
80°
Let \(\angle S = x\). Then \(\angle R = 2x\), \(\angle Q = \tfrac{\angle R}{4} = \tfrac{x}{2}\), and \(\angle P = 2\angle Q = x\).
Sum of angles in a quadrilateral: \(\angle P+\angle Q+\angle R+\angle S = 360^\circ\).
\(x+\tfrac{x}{2}+2x+x = 4.5x = 360 \Rightarrow x=80\).
Hence, the value of \(\angle S\) is 80°.
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