Question

1. if (mangle efh=(5x + 1)^{circ}), (mangle hfg = 62^{circ}), and (mangle efg=(18x + 11)^{circ}), find each measure.

Explanation:

Step1: Use angle - addition postulate

Since $\angle EFG=\angle EFH+\angle HFG$, we can set up the equation $(18x + 11)=(5x + 1)+62$.

Step2: Simplify the right - hand side of the equation

$(5x + 1)+62=5x+63$. So the equation becomes $18x + 11=5x+63$.

Step3: Isolate the variable terms

Subtract $5x$ from both sides: $18x-5x + 11=5x-5x+63$, which simplifies to $13x + 11=63$.

Step4: Isolate the variable

Subtract 11 from both sides: $13x+11 - 11=63 - 11$, getting $13x=52$.

Step5: Solve for x

Divide both sides by 13: $x=\frac{52}{13}=4$.

Step6: Find $m\angle EFH$

Substitute $x = 4$ into the expression for $m\angle EFH$: $m\angle EFH=(5x + 1)=(5\times4+1)=21^{\circ}$.

Step7: Find $m\angle EFG$

Substitute $x = 4$ into the expression for $m\angle EFG$: $m\angle EFG=(18x + 11)=(18\times4+11)=83^{\circ}$.

Answer:

$x = 4$, $m\angle EFH=21^{\circ}$, $m\angle EFG=83^{\circ}$