Question

solve for x.
2x
-10 + 2x
m s l
○ a. 10
○ b. 12
○ c. 3
○ d. 8

Explanation:

Step1: Identify similar - triangles

Since $\triangle KML$ and $\triangle KRL$ have side - length relationships (the marked equal segments suggest similarity), and by the mid - segment theorem or similar - triangle properties, we can set up an equation. Here, we assume that $RS$ is parallel to $ML$ and $S$ is the mid - point of $ML$. Then $\frac{KR}{KL}=\frac{KS}{KM}$. In this case, we can also use the fact that if we consider the ratios of corresponding sides, we know that $KS = - 10 + 2x$ and $KM=2x$. And from the equal - segment markings, we can assume a relationship based on similar triangles. Let's set up an equation based on the fact that the ratio of corresponding sides of similar triangles is equal. If we assume the smaller triangle formed by $R$ and $S$ is similar to the larger one, we have $2(-10 + 2x)=2x$.

Step2: Solve the equation

First, expand the left - hand side:
$2(-10 + 2x)=-20 + 4x$. So the equation becomes $-20 + 4x=2x$.
Subtract $2x$ from both sides: $-20 + 4x-2x=2x-2x$, which simplifies to $-20 + 2x = 0$.
Then add 20 to both sides: $2x=20$.
Divide both sides by 2: $x = 10$.

Answer:

A. 10