Question

Derek wrote the following paragraph proof for the Vertical Angles Theorem:

Line segment NT intersects line segment MR forming four angles. Angles 1 and 3 are vertical angles. Angles 2 and 4 are vertical angles.

The sum of angle 1 and angle 4 and the sum of angle 3 and angle 4 are each equal to 180 degrees by the definition of supplementary angles. The sum of angle 1 and angle 4 is equal to the sum of angle 3 and angle 4 by the transitive property of equality. Angle 1 is equal to angle 3 _____________________.

Which phrase completes the proof?

Answer 1

The answer would be Angle 1 is equal to angle 3 by the subtraction property of equality.

Answer 2

The phrase that would complete the proof is this:
Angle 2 is equal to Angle 4.

Vertical angles are angles formed when two lines intersect each other. The angles that are opposite each other are equal by a series of supplementary, complementary, and transitive property proofs.