Proving Lines Are Parallel

Question

Given: p ll q; <1 and <4 are supplementary

Prove: r ll s

The picture is in here and have to use all lines:

https://drive.google.com/drive/folders/13ODk_8fNotUI44tiH5IaXliy8KgYt6OG?usp=sharing

Answer 1

angle 1 + angle 2 = 180 becuase they are supplementary

angle 1 + angle 4 = 180 becuase they given to be supplementary

subtracting these equations: angle2 - angle4 = 0

so angle2 = angle 4

But angle4 = angle5 becuase they are vertical angles

angle5 = angle6 becuase p || q

So angle2 = angle4 = angle5 = angle6

By converse parallel line theorem, r || s,

since angle2=angle