ABCD is a quadrilateral in which angle A is 90°.Is ABCD a rectangle?

1. Angle B+Angle D =180°
2. The quadrilateral ABCD is a parallelogram.

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(1) \(\angle B + \angle D = 180°\).
So, \(\angle A + \angle C = 90°\), but B and D could be anything totaling to 180.

(2) The quadrilateral ABCD is a parallelogram.
If ABCD is a parallelogram, opposite angles are equal, so \(\angle A = \angle C = 90°\).
\(\angle B = \angle D\), and their sum should be 180, so \(\angle B = \angle D=90°\)
Thus ABCD is a rectangle for sure, and if its sides are equal, it may even be square.
Suff

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