Question

Prove below?

Given: `angle 2` and `angle 3` are supplementary

Prove: `angle 1` and `angle 4` are supplementary

Answer 1

See below.

Explanation:

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

[1] `angle 2 + angle 3 = 180^o`

We can use the vertical angle theorem to obtain

[2] `angle 4 = angle 2`

and

[3] `angle 1 = angle 3`

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

`angle 4+angle 1 = 180^o`

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