Question

∠efg and ∠gfh are a linear - pair, m∠efg = 2n + 19, and m∠gfh = 4n + 29. what are m∠efg and m∠gfh? m∠efg = m∠gph = (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, $(2n + 19)+(4n + 29)=180$.

Step2: Combine like - terms

$2n+4n+19 + 29=180$, which simplifies to $6n+48 = 180$.

Step3: Solve for $n$

Subtract 48 from both sides: $6n=180 - 48=132$. Then divide both sides by 6: $n=\frac{132}{6}=22$.

Step4: Find $m\angle EFG$

Substitute $n = 22$ into the expression for $m\angle EFG$: $m\angle EFG=2n + 19=2\times22+19=44 + 19=63^{\circ}$.

Step5: Find $m\angle GFH$

Substitute $n = 22$ into the expression for $m\angle GFH$: $m\angle GFH=4n + 29=4\times22+29=88 + 29=117^{\circ}$.

Answer:

$m\angle EFG = 63^{\circ}$, $m\angle GFH = 117^{\circ}$