Question

If someone have all the proofs of this I’ve been trying since yesterday PLEASE

Answer 1

Please see steps below

Explanation:

Notice the following:

(a) Angles 5 and 1 are alternate angles between parallel lines, and then they must be congruent (equal in measure)
`\angle 1 \,=\,\angle 5`

(b) Angles 6 and 3 are also alternate angles between parallel lines, so they must be congruent (equal measure)
`\angle 3 \,=\,\angle 6`

Therefore, instead of expressing the addition:

`\angle 5\,\,+\,\,\angle 2\,\,+\,\,\angle 6`

we can write:

`\angle 1\,\,+\,\,\angle 2\,\,+\,\,\angle 3`

which in fact clearly add to
`180^o`