Answer:
![\angle6=123](https://img.qammunity.org/2021/formulas/mathematics/high-school/i07671dr3956de14jap6hmln0fa0ljhs02.png)
Explanation:
Given
Lines x and y
Transversal b
![\angle 1 = 57](https://img.qammunity.org/2021/formulas/mathematics/high-school/qy5wllkx6koijy66koyq7l9tycsfr1ie63.png)
Required
Find
![\angle 6](https://img.qammunity.org/2021/formulas/mathematics/college/6y1r93grm4c34u6whruch633qjktjd8ndy.png)
From the attachment,
and
are vertically opposite.
This means that
![\angle 1 =\angle 7 = 57](https://img.qammunity.org/2021/formulas/mathematics/high-school/r54u6fyl40sb82bo27qsntxjjign8zovyp.png)
Similarly
and
are supplementary angles
So:
![\angle7 + \angle6=180](https://img.qammunity.org/2021/formulas/mathematics/high-school/u22fnjo98asybdvvenhma36r4fcx3yrcyr.png)
Make
the subject
![\angle6=180-\angle7](https://img.qammunity.org/2021/formulas/mathematics/high-school/uk4gfnyt0cs0ew30w5fw02f5808l8pp76v.png)
![\angle6=180-57](https://img.qammunity.org/2021/formulas/mathematics/high-school/27dz5lp6ggg68ibwkcmqzamk3vewvpzkgy.png)
![\angle6=123](https://img.qammunity.org/2021/formulas/mathematics/high-school/i07671dr3956de14jap6hmln0fa0ljhs02.png)
The relationship between
and
is that they are supplementary angles because:
![\angle6+ \angle1=180](https://img.qammunity.org/2021/formulas/mathematics/high-school/nlwaie4a5xyof0m2pqi7opy985q7x9dh33.png)