Question

quadrilateral abcd is a parallelogram. select one pair of equal angles.

Explanation:

Step1: Recall parallelogram angle property

In a parallelogram, opposite angles are equal, and consecutive angles are supplementary. Also, alternate - interior angles formed by a transversal are equal. For parallelogram \(ABCD\), \(AB\parallel CD\) and \(AD\parallel BC\).

Step2: Identify equal angles

Looking at the angles, \(\angle B\) and \(\angle D\) are opposite angles? No, wait, \(\angle B\) and \(\angle D\) are the acute angles, and \(\angle A\) and \(\angle C\) are the obtuse angles. Also, since \(AB\parallel CD\) and \(BC\) is a transversal, \(\angle B=\angle D\) (alternate - interior angles) or \(\angle A = \angle C\) (opposite angles of parallelogram). Another way, from the diagram, \(\angle B\) and \(\angle D\) are equal (the small blue - shaded angles), and \(\angle A\) and \(\angle C\) are equal (the large blue - shaded angles). So one pair of equal angles is \(\angle B=\angle D\) (or \(\angle A=\angle C\)).

Answer:

\(\angle B = \angle D\) (or \(\angle A=\angle C\))