Question

∠efg and ∠gfh are a linear pair, m∠efg = 2n + 16, and m∠gfh = 5n + 24. what are m∠efg and m∠gfh?
m∠efg =
°
m∠gfh =
°
(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, $(2n + 16)+(5n + 24)=180$.

Step2: Combine like - terms

Combine the $n$ terms and the constant terms: $2n+5n+16 + 24=180$, which simplifies to $7n+40 = 180$.

Step3: Solve for $n$

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

Step4: Find $m\angle EFG$

Substitute $n = 20$ into the expression for $m\angle EFG$: $m\angle EFG=2n + 16=2\times20+16=40 + 16=56^{\circ}$.

Step5: Find $m\angle GFH$

Substitute $n = 20$ into the expression for $m\angle GFH$: $m\angle GFH=5n + 24=5\times20+24=100 + 24=124^{\circ}$.

Answer:

$m\angle EFG = 56^{\circ}$
$m\angle GFH = 124^{\circ}$