SOLUTION: Given: Angle 1 and Angle 2 are complementary. Angle 2 and Angle 3 are supplementary. Prove: Angle 1 and Angle 3 are congruent. Is this possible or is this an error in the

Question 511217: Given:
Angle 1 and Angle 2 are complementary.
Angle 2 and Angle 3 are supplementary.
Prove: Angle 1 and Angle 3 are congruent.
Is this possible or is this an error in the question? If both sets were complementary or supplementary, the proof is straight forward. But with one set complementary and the other supplementary, how can Angle 1 and Angle 3 have the same measure?
Found 2 solutions by solver91311, richard1234:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Nope, impossible situation. Angle 2 complementary to Angle 1 implies that both Angle 2 and Angle 1 are less than 90 in measure. Angle 2 being less than 90 means that supplementary Angle 3 must be greater than 90. Hence 3 and 1 cannot possibly be congruent.

John

My calculator said it, I believe it, that settles it

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
The question is impossible. The other tutor's explanation of why it's impossible is correct. Alternatively, you can let Angle 1 = x, Angle 2 = 90-x, and Angle 3 = 180 - (90-x) = 90+x. It is obviously impossible for x to equal 90+x.
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