Question

What is the Length of CG

Answer 1

Answer: 32

Step-by-step 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,

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