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# are all linear pairs supplementary angles

From Wikipedia

Supplementary angles

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 non-shared 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&nbsp;âˆ’&nbsp;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.

Question:You discovered that if a pair of angles is a linear pair then the angles are supplementary. Does that mean that all supplementary angles form a linear pair of angles? Is the converse true? If not, give a counterexample.

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.

Question:Yeah can someone please explain what a linear pair is.OF ANGLES. because i took a test and it said to explain why the following statment is false: If two angles makes a supplementary angle, then they do not make linear pair.

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.

Question:If two angles are supplementary, then they are a linear pair of angles ? True or False

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 non-shared sides form a line. Hope you understand this.

Question:Choose the converse of the following conditional statement If two angles form a linear pair, then they are supplementary a.If two angles are supplementary, then they form a linear pair b.If two angles are not supplementary, then they do not form a linear pair c.If two angles do not form a linear pair, then they are supplementary.

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.