Mathematics ACT Aspire Practice Test

Which of the following statements about vertical angles is true?

1. They are always adjacent.

2. They are always congruent.

3. They add up to 90 degrees.

4. They are formed by perpendicular lines.

The correct answer is: They are always congruent.

Vertical angles are the angles opposite each other when two lines intersect. By definition, vertical angles are always congruent, meaning they have the same measure. This property arises from the way angles are formed; when two lines cross, each pair of opposite angles will always be equal. If we consider the other statements, they do not hold true. For example, vertical angles are not adjacent; they are located across from each other, which inherently means they are not next to each other. They also do not always add up to 90 degrees; they can vary in degree measure but will always be equal. Lastly, while vertical angles can be formed where two lines intersect, they are not specifically a result of perpendicular lines; perpendicular lines form right angles, not necessarily vertical angles. Therefore, the statement about vertical angles being congruent is the only correct one.