The triangles are similar by the AA Similarity Postulate. Find the value of x.

Question

7.5 15 18 x

27

1.2

12

270

Answer 1

To solve for $x$ using the AA (Angle-Angle) Similarity Postulate, we know that the triangles are similar, meaning their corresponding sides are proportional.

Given:
1. One pair of corresponding sides is $7.5$ and $15$.
2. Another pair of corresponding sides is $18$ and $x$.

Let's set up the proportion:
$$\frac{7.5}{15}=\frac{18}{x}$$

First, simplify $\frac{7.5}{15}$:
$$\frac{7.5}{15}=\frac{1}{2}$$

So the proportion can be rewritten as:
$$\frac{1}{2}=\frac{18}{x}$$

Next, solve for $x$ by cross-multiplying:
$$1\cdot x=2\cdot 18$$
$$x=36$$

Thus, the value of $x$ is $36$.