In the quadrilateral BCOE, the sides BC and OE are parallel and the angles B and O are 90.

In the quadrilateral BCOE, the sides BC and OE are parallel and the angles B and O are 90. Is the quadrilateral BCOE a parallelogram?

A sufficient condition for a quadrilateral to belong to a parallelogram is the presence of pairwise parallel opposite sides.
In our case, the sides BC and OE are parallel, but this is not directly said about the other sides.
If angles B and O are straight, then angles C and E must also be right, which means that the sides BE and CO are also parallel.
From this we conclude that the BCOE quadrangle is a parallelogram and, moreover, a straight parallelogram, that is, a rectangle.
ANSWER: yes, it is.