Question

1. m∠gfn = 4x + 10, m∠nfe = 14x + 3, and m∠gfe = 157°. find m∠nfe.

Explanation:

Step1: Use angle - addition postulate

Since $\angle GFE=\angle GFN+\angle NFE$, we have the equation $(4x + 10)+(14x + 3)=157$.

Step2: Combine like - terms

$4x+14x+10 + 3=157$, which simplifies to $18x+13 = 157$.

Step3: Isolate the variable term

Subtract 13 from both sides: $18x=157 - 13$, so $18x=144$.

Step4: Solve for x

Divide both sides by 18: $x=\frac{144}{18}=8$.

Step5: Find $m\angle NFE$

Substitute $x = 8$ into the expression for $m\angle NFE$. $m\angle NFE=14x+3=14\times8 + 3$.
$m\angle NFE=112 + 3=115^{\circ}$.

Answer:

$115^{\circ}$