According to the Vertical Angles Theorem, which property holds for vertical angles?

According to the Vertical Angles Theorem, which property holds for vertical angles?

• A. Vertical angles are perpendicular
• B. Vertical angles have congruent angle measures
• C. Vertical angles are supplementary
• D. Vertical angles are complementary

Answer: (B)

Vertical angles formed by two intersecting lines are congruent. When the lines cross, the angles that are opposite each other share the same rays in opposite directions, so rotating one angle around the intersection aligns it with the other and their measures are the same. This means the key property is that vertical angles have equal measures, regardless of how large or small those angles are. For example, if one angle is 40 degrees, its opposite angle is also 40 degrees; the other pair of angles at the intersection would be 140 degrees each since adjacent angles are supplementary. Vertical angles don’t have to be perpendicular, and they aren’t inherently supplementary to each other—it's the adjacent angles that sum to 180.

Vertical angles formed by two intersecting lines are congruent. When the lines cross, the angles that are opposite each other share the same rays in opposite directions, so rotating one angle around the intersection aligns it with the other and their measures are the same. This means the key property is that vertical angles have equal measures, regardless of how large or small those angles are. For example, if one angle is 40 degrees, its opposite angle is also 40 degrees; the other pair of angles at the intersection would be 140 degrees each since adjacent angles are supplementary. Vertical angles don’t have to be perpendicular, and they aren’t inherently supplementary to each other—it's the adjacent angles that sum to 180.