Question

∠efg and ∠gfh are a linear pair, m∠efg = 3n + 25, and m∠gfh = 5n + 35. what are m∠efg and m∠gfh? m∠efg = (square^{circ}) m∠gfh = (square^{circ}) (simplify your answers.)

Explanation:

Step1: Recall linear - pair property

Since $\angle EFG$ and $\angle GFH$ are a linear pair, $m\angle EFG + m\angle GFH=180^{\circ}$. So, $(3n + 25)+(5n + 35)=180$.

Step2: Combine like - terms

$3n+5n+25 + 35=180$, which simplifies to $8n+60 = 180$.

Step3: Solve for $n$

Subtract 60 from both sides: $8n=180 - 60$, so $8n=120$. Then divide both sides by 8: $n=\frac{120}{8}=15$.

Step4: Find $m\angle EFG$

Substitute $n = 15$ into the expression for $m\angle EFG$: $m\angle EFG=3n + 25=3\times15+25=45 + 25=70^{\circ}$.

Step5: Find $m\angle GFH$

Substitute $n = 15$ into the expression for $m\angle GFH$: $m\angle GFH=5n + 35=5\times15+35=75+35 = 110^{\circ}$.

Answer:

$m\angle EFG = 70^{\circ}$
$m\angle GFH = 110^{\circ}$