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A parallelogram is a quadrilateral and so its internal angles must sum to 360o.

An acute angle is one of less than 90o.

If all 4 angles of a parallelogram are acute, they are all less than 90o and so sum to less than 4 x 90o = 360o.

But they must sum to exactly 360o. Thus they cannot all be acute.

For a parallelogram opposite angles are equal; so 2 are acute and 2 are obtuse (or all are right angles - 90o).

Note that a rectangle is a special case of the parallelogram in which all angles are 90o.

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