Question

∠efg and ∠gfh are a linear pair, m∠efg = 4n + 18, and m∠gfh = 3n + 22. what are m∠efg and m∠gfh?
m∠efg = □°
m∠gfh = □°
(simplify your answers.)

Explanation:

Step1: Use linear - pair property

Since $\angle EFG$ and $\angle GFH$ are a linear pair, $m\angle EFG + m\angle GFH=180^{\circ}$. So, $(4n + 18)+(3n + 22)=180$.

Step2: Combine like - terms

Combine the $n$ terms and the constant terms: $4n+3n+18 + 22=180$, which simplifies to $7n+40 = 180$.

Step3: Solve for $n$

Subtract 40 from both sides: $7n=180 - 40$, so $7n=140$. Then divide both sides by 7: $n=\frac{140}{7}=20$.

Step4: Find $m\angle EFG$

Substitute $n = 20$ into the expression for $m\angle EFG$: $m\angle EFG=4n + 18=4\times20+18=80 + 18=98^{\circ}$.

Step5: Find $m\angle GFH$

Substitute $n = 20$ into the expression for $m\angle GFH$: $m\angle GFH=3n + 22=3\times20+22=60 + 22=82^{\circ}$.

Answer:

$m\angle EFG = 98^{\circ}$
$m\angle GFH = 82^{\circ}$