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Question 1107545: 1. Which of the following is the best definition of a linear pair of angles? (1 point)
a) A linear pair is a pair of angles whose measures sum to 180 degrees and share a common ray.
b) A linear pair is a pair of angles with a common vertex whose sum is 180.
c) A linear pair is a pair of angles with a common vertex and sides that are opposite rays.
d) A linear pair is a pair of adjacent angles with no interior points in common.
My Answer: C
Could someone please check my answer?
Answer by greenestamps(13195)   (Show Source):
You can put this solution on YOUR website!
I would not consider any of the choices a valid definition of a linear pair.
(a) -- Not sufficient, because the shared ray could be the "initial" side of both angles. To complete this definition, you would have to say the two angles have no internal points in common.
(b) -- Not sufficient, because this definition does not require that the angles share a common ray.
(c) -- Not sufficient. When two lines intersect, the angles in a linear pair have sides that are opposite rays; but the vertical angles formed by the two intersecting lines also have sides that are opposite rays. Each linear pair has one pair of sides that are opposite rays; each vertical pair has two pairs of sides that are opposite rays. So you could fix this definition by saying the pair of angles has only one pair of sides that are opposite rays, but that makes for a very awkward definition.
(d) -- Not sufficient, because it says nothing about the sum of the angles being 180 degrees.
The way you ask the question, it appears to be a question from an assignment or a test. Good luck on choosing the "best" of the four insufficient definition choices.
A simple definition only needs to say that the angles are adjacent and supplementary. The "adjacent" takes care of the shared ray and no internal points in common; the supplementary takes care of the sum being 180 degrees.
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