Question

What is the Length of CG

Answer 1

Answer: 32

Explanation:

Since
`\overline{FG} \parallel \overline{AC}`, we know that by the corresponding angles theorem,
`\angle BFG \cong \angle BAC` and
`\angle BGF \cong \angle BCA`.

Thus,
`\triangle BFG \sim \triangle BAC` by AA.

It follows that since corresponding sides of similar triangles are proportional,

`(36+90)/(90)=(CG+80)/(80)\\ \\(126)/(90)=(CG+80)/(80)\\\left((126)/(90) \right)(80)=CG+80\\112=CG+80\\CG=\boxed{32}`