Question

find the measure of ∠gcf.

Explanation:

Step1: Set up equation

Since $\angle GCF$ and $\angle PCT$ are vertical - angles, they are equal. So we set $3f + 37=8f + 27$.

Step2: Solve for $f$

Subtract $3f$ from both sides: $37 = 8f-3f + 27$, which simplifies to $37 = 5f+27$. Then subtract 27 from both sides: $37 - 27=5f$, so $10 = 5f$. Divide both sides by 5, we get $f = 2$.

Step3: Find measure of $\angle GCF$

Substitute $f = 2$ into the expression for $\angle GCF$: $\angle GCF=3f + 37$. So $\angle GCF=3\times2+37=6 + 37=43$.

Answer:

$43$