Discussion
In a parallelogram PQRS, ∠ P = 2x + 20°, ∠ Q = 2y - 40°, ∠ R = 5x - 100° and ∠ S = 3y - 100°. Then, the value of (x + y) is equal to :
Answer: A
The value of \(x + y\) is 100.
In a parallelogram opposite angles are equal, so \(\angle P = \angle R\) and \(\angle Q = \angle S\):
\[ \begin{aligned} 2x + 20 &= 5x - 100 \Rightarrow x = 40 \\ 2y - 40 &= 3y - 100 \Rightarrow y = 60 \end{aligned} \]
So \(x + y = 100\). Check: the angles are \(P = R = 100^{\circ}\) and \(Q = S = 80^{\circ}\); adjacent angles add to \(180^{\circ}\) and all four add to \(360^{\circ}\), as they must. The other options come from using the wrong pairs of angles.
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