Question

URGENT NEED HELP

Given: Angle 1 and angle 2 are supplementary.
Angle 3 and angle 4 are supplementary.
Angle 1 is congruent to angle 3.
Prove: Angle 2 is congruent to angle 4.

Answer 1

Let us try to do it by steps:

1) Angle 2 is supplementary to Angle 3
Reason: angle 2 is supplementary to angle 1 which is congruent to angle 3.
2) Angles 4 and 2 are both supplementary to angle 3.
Reason: One is given, also see the above.
3) Angles 4 and 2 are congruent.
Reason: They are supplementary to the same angle. Hence, they form a straight line with the same angle. In algebra, we have that A2+A3=180 and A4+A3=180 (180 are the degrees of a straight angle). Hence, we can infer that A2=A4=180-A3.