Question

Given: angle 1 and angle 2 form a linear pair; angle 2 is congruent to angle 4 Prove: angle 1 and angle 3 are supplementary

Answer 1

Angle 1 and angle 3 are supplementary because angle 1 and angle 2 form a linear pair and angle 2 is congruent to angle 4.

Step-by-step explanation:

Let angle 1 and angle 2 form a linear pair, meaning that they are adjacent angles that add up to 180 degrees.

Since angle 2 is congruent to angle 4, angle 2 and angle 4 have the same measure and are congruent.

Since angle 1 and angle 2 form a linear pair and angle 2 is congruent to angle 4, we can conclude that angle 1 and angle 3 are supplementary because supplementary angles add up to 180 degrees.