Question

Keaton wrote the following paragraph proof for the Vertical Angles Theorem: The sum of angle 1 and angle 4 and the sum of angle 3 and angle 4 are each equal to 180 degrees _______________. 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 by the subtraction property of equality. Which phrase completes the proof?

Answer 1

Answer: by the def of supplementary angles

Step-by-step explanation: the definition for supplementary angles are "two angles that add up to 180 degrees".

Since that is true (and non of the other answers make sense) it has to be SUPPLEMENTARY ANGLES.

Answer 2

For the Vertical Angle theorem, if a slant line is intersected by a horizontal, the opposite angles must be equal. In here, he stated that the sum of angle 1 and angle 4 and the sum of angle 3 and angle 4 are each equal to 180 degrees. It means that 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.