Question

find the measure of ∠gkl.
(8x + 11)°
(7x - 41)°
m∠gkl =

Explanation:

Step1: Use vertical - angle property

Since $\angle GKL$ and the angle with measure $(7x - 41)^{\circ}$ are vertical angles, they are equal. Also, $\angle GKL$ and the angle with measure $(8x + 11)^{\circ}$ are supplementary (linear - pair), so $(8x + 11)+(7x - 41)=180$.

Step2: Solve the equation for x

Combine like - terms: $8x+7x+11 - 41 = 180$, which simplifies to $15x-30 = 180$. Add 30 to both sides: $15x=180 + 30=210$. Divide both sides by 15: $x=\frac{210}{15}=14$.

Step3: Find the measure of $\angle GKL$

Substitute $x = 14$ into the expression for $\angle GKL$ (we can use the vertical - angle expression $7x - 41$). So, $m\angle GKL=7x - 41=7\times14-41=98 - 41 = 57$.

Answer:

$57$