SOLUTION: Given: angle AOC and angle COB are a linear pair. Prove: angle AOC and angle COB are a supplementary. Do i just need to say that they are supplementary because they are linear

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Question 144282: Given: angle AOC and angle COB are a linear pair.
Prove: angle AOC and angle COB are a supplementary.
Do i just need to say that they are supplementary because they are linear pairs? Does that mean the same thing?
Answer by solver91311(12126) (Show Source):
You can put this solution on YOUR website!
Linear Pair and Supplementary are not exactly the same thing. A linear pair of angles consists of two angles that are both adjacent and supplementary. For your problem, you can say that the angles are supplementary because they are a linear pair. In other words, if angle AOC and angle COB are a linear pair, then angle AOC and angle COB are supplementary by definition of a linear pair.

Note that the opposite conjecture is not necessarily true. If you were given that the two angles were supplementary, you would also have to prove that they are adjacent in order to prove that they are a linear pair.