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Vertical Angles Theorem

Theorem:Vertical angles are always congruent.

In the figure, 13 and 24.

Proof:

1and2 form a linear pair, so by the Supplement Postulate, they are supplementary. That is,

m1+m2=180°.

2and3 form a linear pair also, so

m2+m3=180°.

Subtracting m2 from both sides of both equations, we get

m1=180°m2=m3.

Therefore,

13.

You can use a similar argument to prove that 24.