Question

State the reason for the conclusion.

Given: <4 and <5 are vertical angles
Conclusion: <4 congruent <5

A. Vertical angles are always congruent.
B. Vertical angles are supplementary.
C. Vertical angles are equal in measure.
D. Vertical angles are parallel.

Answer 1

The reason why angles 4 and 5 are congruent is because vertical angles are always congruent, resulting from the properties of intersecting lines.

Step-by-step explanation:

The question asks for the reason why angles 4 and 5 are congruent given that they are vertical angles. The correct answer is A. Vertical angles are always congruent. Vertical angles are the angles opposite each other when two lines cross. They are called "vertical" because they share the same vertex (corner point), not because they are up/down. Vertical angles are equal in measure because they are formed by the same pairs of lines and due to the properties of intersecting lines, these angles are always congruent.