Question

explain why the triangles are similar. then find the distance represented by x.
why are the triangles similar? choose the correct answer below.
a. there is a pair of congruent vertical angles and the sides that include the two vertical angles are also congruent, so the triangles are similar.
b. there is a pair of congruent vertical angles and the sides that include the two vertical angles are proportional, so the triangles are similar by
c. there is a pair of congruent vertical angles and the sides that include the two vertical angles are proportional, so the triangles are similar by
d. the corresponding sides of two triangles are proportional, so the triangles are similar by the sss - theorem.
e. there is a pair of congruent vertical angles and a pair of congruent right angles, so the triangles are similar by the aa - postulate.
x = ft (type an integer or a simplified fraction.)

Explanation:

Step1: Identify similarity criterion

There is a pair of congruent vertical angles and a pair of congruent right - angles. So, the triangles are similar by the AA - Postulate.

Step2: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. We have the proportion $\frac{180}{90}=\frac{x}{120}$.

Step3: Solve for x

Cross - multiply: $180\times120 = 90x$. Then $x=\frac{180\times120}{90}$. Simplify the right - hand side: $x = 240$.

Answer:

240