Final Answer:
The measure of each numbered angle and the theorem name that justifies the work is (A) angle1 = x, angle2 = x - 6, Vertical Angles Theorem.
Step-by-step explanation:
The Vertical Angles Theorem states that when two lines intersect, the vertical angles formed are congruent. In this case, angle1 and angle2 are vertical angles as they are opposite each other when the lines intersect. Therefore, the measure of angle1 is x, and the measure of angle2 is x - 6.
The given information establishes that angle1 and angle2 are vertical angles, which means they are congruent. The Vertical Angles Theorem justifies that when two lines intersect, the angles formed opposite each other are equal in measure. In this scenario, angle1 (m angle1) is represented by x, and angle2 (m angle2) is represented by x - 6. This aligns with the Vertical Angles Theorem, making option (A) the correct choice.
Understanding angle relationships and the theorems that govern them is fundamental in geometry. Recognizing the characteristics of vertical angles allows us to determine their measures based on the given information.
In summary, the correct answer is (A) angle1 = x, angle2 = x - 6, Vertical Angles Theorem, which asserts that vertical angles formed by intersecting lines are congruent.