Prove the second case of the congruent supplements theorem where two angles are supplementary to congruent angles.

Given: <1 and <2 are supplements;

<3 and <4 are supplements;

<2 `~=` <3

Prove:

<1 `~=` <4

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It is given that `/_ 1` and` /_ 2` are supplementary.

`/_1 + /_2 = 180`

=> `/_2 = 180 - /_1`

Also, `/_3 + /_4 = 180`

=> `/_3 = 180 - /_4`

`/_ 2 ~= /_3`

=> `180 - /_1 ~= 180 - /_4`

=>` /_1 ~= /_4`

**This shows that `/_1 ~= /_4` **

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Thank you very much!

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