Question

current skill $ find the measure of ∠kpg.

Explanation:

Step1: Set up an equation

Assume $\angle KPG$ and $\angle GPM$ are adjacent - angles and $\angle KPM$ is a straight - angle (180°). So, $(5y + 4)+(8y-18)=180$.

Step2: Combine like terms

$5y+8y+4 - 18=180$, which simplifies to $13y-14 = 180$.

Step3: Solve for y

Add 14 to both sides of the equation: $13y=180 + 14=194$. Then $y=\frac{194}{13}$.

Step4: Find the measure of $\angle KPG$

Substitute $y$ into the expression for $\angle KPG$. $\angle KPG=5y + 4=5\times\frac{194}{13}+4=\frac{970}{13}+\frac{52}{13}=\frac{970 + 52}{13}=\frac{1022}{13}\approx78.62°$.

Answer:

$\frac{1022}{13}$ (or approximately $78.62°$)