Question

m∠gfn = 4x + 10, m∠nfe = 14x + 3, and m∠gfe = 157°. given the information above, set up an equation to solve for x and find x. equation x=

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: $x=\frac{144}{18}=8$.

Answer:

Equation: $4x + 10+14x + 3 = 157$
$x = 8$