Question

figure pqrs is a parallelogram. what are the measures of angles p and s? ∠p = 20°; ∠s = 160° ∠p = 40°; ∠s = 140° ∠p = 140°; ∠s = 40° ∠p = 160°; ∠s = 20°

Explanation:

Answer:

In a parallelogram, adjacent - angles are supplementary, so \(\angle Q+\angle R = 180^{\circ}\), then \((x + 15)+(6x-10)=180\).
Combining like - terms gives \(7x + 5 = 180\), \(7x=175\), and \(x = 25\).
\(\angle Q=x + 15=25 + 15 = 40^{\circ}\), \(\angle R=6x-10=6\times25-10 = 140^{\circ}\).
\(\angle P=\angle R = 140^{\circ}\) (opposite angles of a parallelogram are equal) and \(\angle S=\angle Q = 40^{\circ}\) (opposite angles of a parallelogram are equal).
So the answer is: \(\angle P = 140^{\circ};\angle S = 40^{\circ}\)