Prove below?

Question

Given: $∠ 2$ $angle 2$ and $∠ 3$ $angle 3$ are supplementary

Prove: $∠ 1$ $angle 1$ and $∠ 4$ $angle 4$ are supplementary

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Answer 1 · 2018-05-18T02:53:06

See below.

We are given that $∠ 2$ $angle 2$ and $∠ 3$ $angle 3$ are supplementary, which means

[1] $∠ 2 + ∠ 3 = 180^{o}$ $angle 2 + angle 3 = 180^o$

We can use the vertical angle theorem to obtain

[2] $∠ 4 = ∠ 2$ $angle 4 = angle 2$

and

[3] $∠ 1 = ∠ 3$ $angle 1 = angle 3$

Now we substitute [2] and [3] into [1]

$∠ 4 + ∠ 1 = 180^{o}$ $angle 4+angle 1 = 180^o$

Which by definition means that $∠ 4$ $angle 4$ and $∠ 1$ $angle 1$ are supplementary.