Question

find the value of x.

Explanation:

Step1: Set up angle - sum equation

We know that the sum of the two non - overlapping angles $\angle KNL$ and $\angle LNM$ equals $\angle KNM$. So, $42+(10x - 3)=89$.

Step2: Simplify the left - hand side

First, simplify the left - hand side of the equation: $42+10x-3=10x + 39$. So the equation becomes $10x+39 = 89$.

Step3: Isolate the variable term

Subtract 39 from both sides of the equation: $10x+39-39=89 - 39$, which gives $10x=50$.

Step4: Solve for x

Divide both sides of the equation by 10: $\frac{10x}{10}=\frac{50}{10}$, so $x = 5$.

Answer:

$5$