Question

Can a quadrilateral ABCD be a parallelogram, if:
$\angle D+\angle B={180}^{\circ }$ ?

Answer 1

Yes, $\angle D+\angle B={180}^{\circ }$ can be true in a parallelogram. However, since $\angle D$ and $\angle B$ are opposite angles, they would be equal.

$\angle D+\angle B={180}^{\circ }\Rightarrow 2\angle D={180}^{\circ }\Rightarrow \angle D=\angle B=\frac{{180}^{\circ }}{2}={90}^{\circ }$
Such a parallelogram would be a rectangle.