Show that each angle of a rectangle is a right angle.

(N/A) Let us recall what a rectangle is.
$A$ rectangle is a parallelogram in which one angle is a right angle.
Let $ABCD$ be a rectangle in which $\angle A = 90^{\circ}$.
We have to show that $\angle B = \angle C = \angle D = 90^{\circ}$.
We have $AD \parallel BC$ and $AB$ is a transversal.
So,$\angle A + \angle B = 180^{\circ}$ (Interior angles on the same side of the transversal are supplementary).
But,$\angle A = 90^{\circ}$.
So,$\angle B = 180^{\circ} - \angle A = 180^{\circ} - 90^{\circ} = 90^{\circ}$.
Now,$\angle C = \angle A$ and $\angle D = \angle B$ (Opposite angles of a parallelogram are equal).
So,$\angle C = 90^{\circ}$ and $\angle D = 90^{\circ}$.
Therefore,each of the angles of a rectangle is a right angle.