Question

In parallelogram $PQRS,\angle Q=(4x-5{)}^o$ and $\angle S=(3x+10{)}^o$, then find $\angle Q$ and $\angle R$.

Answer 1

In a parallelogram, opposite angle are equal

$\Rightarrow \angle Q=\angle s\Rightarrow 4x-5=3x+10\Rightarrow x=15$

Also sum of adjacent angles is ${180}^o\Rightarrow \angle Q+\angle R={180}^o$

$\Rightarrow 4\left(15\right)-5+\angle R=180$

$\Rightarrow \angle R={125}^o$, $\angle Q={55}^o$