Given: angle A is and angle C are supplementary; angle B and angle D are supplementary; angle A is congruent to angle B
Prove: angle C is congruent to angle D

Question

Given: angle A is and angle C are supplementary; angle B and angle D are supplementary; angle A is congruent to angle B 
Prove: angle C is congruent to angle D

anonymous · Answer

If two angles are supplementary, they add up to 180 degrees. So,

a + c = 180
b + d = 180

If angle a and angle b are congruent, we can substitute one for the other. Here, I will substitute a for b.

a + c = 180
a + d = 180

We can subtract "a" from both sides of both equations.

c = 180 - a
d = 180 - a

If angle c and angle d are equal to the same thing (180 - a), the angles themselves must have equal measures, and if they have equal measures, they are congruent.

Hope I helped, and let me know if you need anything else or have any more questions! :)