Question

In parallelogram $PQRS$, $\angle P={60}^o$. Find the ratio $\angle R:\angle Q$.

• A. $1:2$
• B. $2:3$
• C. $1:4$
• D. $1:5$

Answer 1

The correct option is A $1:2$

Here $PQRS$ is a parallelogram.

$\angle P={60}^o.$

$\Rightarrow$ $\angle P=\angle R$ [ Opposite angles of parallelogram are equal ]

$\therefore$ $\angle R={60}^o.$ ----- ( 1 )

We know that, in parallelogram sum of adjacent angles are supplementary.

$\therefore$ $\angle P+\angle Q={180}^o.$

$\Rightarrow$ ${60}^o+\angle Q={180}^o.$

$\therefore$ $\angle Q={120}^o.$ ---- ( 2 )

From ( 1 ) and ( 2 ),

$\Rightarrow$ $\frac{\angle R}{\angle Q}=\frac{{60}^o}{{120}^o}=\frac{1}{2}$

$\therefore$ $\angle R:\angle Q=1:2$