SOLUTION: Given: angle 1 and angle 2 form a linear pair angle 2 + angle 3 + angle 4 = 180 Prove: angle 1 = angle 3 and angle4

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Question 132796: Given: angle 1 and angle 2 form a linear pair
angle 2 + angle 3 + angle 4 = 180
Prove: angle 1 = angle 3 and angle4
Answer by solver91311(24713) About Me  (Show Source):
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Linear pairs of angles are supplementary, meaning that the sum of their measures is 180.

That means that a1 + a2 = 180, which we can write as a1 = 180 - a2.

But we also know that a2 + a3 + a4 = 180, which we can write as a3 + a4 = 180 - a2.

Since a = b and c = b if and only if a = c, a3 + a4 = a1.