Question

In a parallelogram PQRS, if $\angle$P is thrice $\angle$Q, find the angles.

Answer 1

Let $\angle Q$ is $x$, then $\angle P$ will be $3x.$

We know that sum of adjacent sides of parallelogram is ${180}^o.$

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

$3x+x={180}^o$

$4x={180}^o$

$x={45}^o$

$\Rightarrow$ $\angle Q={45}^o$

$\Rightarrow$ $\angle P=3\times {45}^o={135}^o$

We know that, opposite angles of a parallelogram are equal.

$\therefore$ $\angle P=\angle R={135}^o$

$\therefore$ $\angle Q=\angle S={45}^o$