Question

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

Answer 1

Answer:

Please see steps below

Step-by-step 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 $180^o$