Not necessarily, but it can.
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Draw a parallelagram this has the opposite sides parallel and no right angles
The answer to this question is a parallelagram
A parallelogram has 0 or 2 acute angles. If the parallelogram happens to have four right-angled corners, it is still a parallelogram (and a rectangle), but no acute angles.
A rectangle or a square.
If I understand the question right I think it's a rhombus or diamond?