Question

Under what conditions must $PQRS$ be a parallelogram?

• A. $x={45}^o$
• B. $y={16}^o$
• C. $x={45}^o,y={16}^o$
• D. $x={16}^o,y={45}^o$

Answer 1

Answer: (C)

$x={45}^o,y={16}^o$

Opposite angles of a parallelogram are equal
$\Rightarrow$ $\angle S=\angle Q$ and $\angle P=\angle R$
$\Rightarrow$ $3x+{42}^o=4x=3^o$ and $6y=5y+{16}^o$
$\Rightarrow$ $x={45}^o$ and $y={16}^o$