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are all linear pairs supplementary angles
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From Wikipedia
Supplementary angles are pairs of angles whose measures add up to 180 degrees. The angles do not have to share a side. If the two supplementary angles are adjacent (i.e. have a common vertex and share just one side), their nonshared sides form a line. The supplement of an angle of 135 degrees is an angle of 45 degrees. The supplement of an angle of x degrees is an angle of 180 âˆ’ x degrees. Supplementary angles do not have to be on the same line, and can be separated in space. For example, adjacent angles of a parallelogram are supplementary.
Trigonometric ratios
The sines of supplementary angles are equal. Theircosines andtangents (unless undefined) are equal in magnitude but have opposite signs.
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Answers:No, not all supplementary angles are a linear pair. A counterexample is: three angles can add up to 180 degrees but that wouldn't be a linear pair. A linear pair is when TWO angles add up to 180. Supplementary angles can also be linear pair but supplementary angles also apply when more than two angles add up to 180. All linear pairs are supplementary angles, but not all supplementary angles are linear pairs.
Answers:A linear pair of angles just means "two angles that add together to form a line." See the picture for an example. Another way to say this is the angles are supplementary and add to 180 . The answer to that question should be FALSE, because if two angles are supplementary, they add to 180 . And then by definition they make a linear pair. In other words, supplementary, add to 180 and linear pair are all synonyms for the same thing. You can't have two angles that are supplementary and not a linear pair.
Answers:A pair of angles are supplementary if their respective measures sum to 180 degrees. If the two supplementary angles are adjacent (i.e. have a common vertex and share a side, but do not have any interior points in common) their nonshared sides form a line. Hope you understand this.
Answers:Statement a is indeed the converse; it's just not valid. While you didn't ask, b is the contrapositive, and true. c is the negation of condition and false.
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