Graduate Management Admission Test (GMAT) Practice Test

What can be said about the angles in a parallelogram?

1. All angles are acute

2. Adjacent angles are equal

3. Opposite angles are equal

4. All angles are right angles

The correct answer is: Opposite angles are equal

In a parallelogram, opposite angles are indeed equal, which makes the statement accurate. This property arises from the nature of parallel lines and transversals. When two pairs of opposite sides are parallel, the angles formed at the intersections with a transversal (the other two sides of the parallelogram) maintain equality; thus, each angle across from another will be the same measure. For instance, if a parallelogram has one angle measuring 70 degrees, the angle directly opposite to it will also measure 70 degrees. Similarly, the adjacent angles will sum up to 180 degrees, adhering to the linear pair postulate. This affirms that while adjacent angles are supplementary, they are not equal, distinguishing the equality of opposite angles as a hallmark of parallelogram properties. In terms of the other options, while all angles being acute or all angles being right angles can be true for certain types of quadrilaterals (like rectangles or rhombuses), they do not apply universally to all parallelograms. Meanwhile, stating that adjacent angles are equal is incorrect as they are supplementary. Thus, the given assertion about opposite angles being equal stands as a fundamental characteristic of all parallelograms.