Question

notice that the triangles shown below are similar by aaa considering the given angle markings as well as the vertical angles. knowing that, find the value of x.

Explanation:

Step1: Set up proportion for similar triangles

Since the triangles are similar, the ratios of corresponding sides are equal. So, $\frac{x + 5}{15}=\frac{10}{12}$.

Step2: Cross - multiply to solve for x

Cross - multiplying gives $12(x + 5)=15\times10$.
First, simplify the right - hand side: $15\times10 = 150$.
Then, expand the left - hand side: $12x+60 = 150$.
Subtract 60 from both sides: $12x=150 - 60=90$.
Divide both sides by 12: $x=\frac{90}{12}=\frac{15}{2}=7.5$.

Answer:

$x = 7.5$