Vertical angles are defined as which of the following?

Vertical angles are defined as which of the following?

• A. A pair of opposite congruent angles formed by intersecting lines
• B. A pair of adjacent angles formed by intersecting lines
• C. Angles formed by a line crossing a circle
• D. Angles inside a triangle

Answer: (A)

Vertical angles are the pair of opposite angles formed when two lines intersect. They are congruent because the four angles around the intersection come in opposite pairs that share the same two lines. A quick way to see it is to note that adjacent angles on a straight line are supplementary (sum to 180 degrees); the angle opposite one of those adjacent angles ends up equal to the first angle. For example, if one angle measures x degrees, the angle opposite it also measures x degrees, while the two adjacent angles measure 180 − x degrees each. This matching of opposite angles being equal is exactly what vertical angles describe. The other choices describe adjacent angles (a linear pair), angles related to circles, or angles inside a triangle, which are different concepts.

Vertical angles are the pair of opposite angles formed when two lines intersect. They are congruent because the four angles around the intersection come in opposite pairs that share the same two lines. A quick way to see it is to note that adjacent angles on a straight line are supplementary (sum to 180 degrees); the angle opposite one of those adjacent angles ends up equal to the first angle. For example, if one angle measures x degrees, the angle opposite it also measures x degrees, while the two adjacent angles measure 180 − x degrees each. This matching of opposite angles being equal is exactly what vertical angles describe. The other choices describe adjacent angles (a linear pair), angles related to circles, or angles inside a triangle, which are different concepts.