Question

Parallelogram $HEAR$
$HE=5cm$
$EA=6cm$
$\angle R={85}^o$

Answer 1

Let us consider,

Parallelogram $HEAR$

In which $HE\parallel AR$

and in which $\angle R={85}^{\circ }$

$\angle E=\angle R$ (opposite angles of parallelogram are equal)

Therefore, $\angle E={85}^{\circ }$

Now,

$\angle A+\angle R={180}^{\circ }$ (sum of co-interiors angle are $180$)

Hence $\angle A={180}^{\circ }-{85}^{\circ }$

Therefore, $\angle A={95}^{\circ }$

and $\angle H=\angle A$ (opposite angles of parallelogram)

$\angle H={95}^{\circ }$

and $HE=AR$ (opposite sides of parallelogram are equal and parallel)

$AR=5cm$

and $EA=HR$ (opposite sides of parallelogram are equal and parallel)

Hence, $HR=6cm$