We know that,
the opposite angles of a parallelogram are equal.
ie. $\angle A=\angle Cand\angle B=\angle D...\left(i\right)$
If they are supplementary as well, then
$\angle A+\angle C={180}^{\circ }$
from (i),
$\angle A+\angle A={180}^{\circ }$
$2\angle A={180}^{\circ }$
$\angle A={90}^{\circ }$
Similarly,
$\angle C={90}^{\circ }$
It means that each angle will be equal to ${90}^{\circ }.$
A parallelogram whose internal angles are all ${90}^{\circ }$ is a rectangle. Thus, the figure will be a rectangle.