What shape has angles that are not right angles and four equal sides?

The shape characterized by four equal sides and angles that are not right angles is a rhomboid. A rhomboid, specifically a type of parallelogram, has opposite sides that are equal and opposite angles that are also equal, but it does not necessarily have right angles. This unique feature differentiates it from other choices.

A square has four equal sides and four right angles, which does not meet the criteria as the angles are specifically right angles. A rectangle, like the square, has equal lengths for opposite sides but also has four right angles. A trapezoid typically has one pair of parallel sides and does not fit the description of having four equal sides. Thus, the defining characteristic of a rhomboid makes it the correct answer for the given question.