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when given is <1 and <2 are linear, what's the reason that <1 and <2 are supplementary?

Answering geometry proofs

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Robert C. | Dr. Robert can help you with Math and ScienceDr. Robert can help you with Math and Sc...
5.0 5.0 (44 lesson ratings) (44)

Let Y be the common vertex for <1 and <2. Let <1 = XYZ and <2 = ZYW. The common ray for these angles is ray YZ.

<1 and <2 are a linear pair -- GIVEN

Ray XY and Ray YW are opposite rays. -- By the definition of a linear pair.

<XYW had measure of 180° -- By the definition of a straight angle (opposite rays)

measure of <1 + measure of <2 = measure of <XYW -- Definition of addition of angle measures

measure of <1 + measure of <2 = 180 -- By substitution

<1 and <2 are supplementary -- By definition of supplementary angles


The logic is <1 and <2 are a linear pair, therefore their non-adjacent sides form opposite rays. Opposite rays have a measure of 180 degrees. The measure of the angle formed by the opposite rays is just the sum of the measures of <1 and <2. The sum of the measures of <1 and <2 are therefore 180 degress. Thus <1 and <2 are supplementary.




Scott W. | Math, Science, and English Tutor, College Counselor.Math, Science, and English Tutor, Colleg...
4.9 4.9 (330 lesson ratings) (330)

Supplementary angles add up to 180 degrees.  When placed next to one another, two supplementary angles form a 180 degree angle.

A 180 degree angle is a line.

If two angles are linear, then by definition, they are two angles placed next to one another, that form a straight line.  That is, the two angles sum to 180 degrees, so they are therefore supplementary.