Question

find the values of x and y.
find x select the correct choice below and, if necessary, fill in the answer box to
complete your choice
a. the value of x is 21
(type an integer or a decimal)
b. the value of x cannot be determined because the triangles are not similar
find y select the correct choice below and, if necessary, fill in the answer box to
complete your choice
a. the value of y is
(type an integer or a decimal)
b. the value of y cannot be determined because the triangles are not similar

Explanation:

Step1: Check similarity of triangles

Since the triangles have two pairs of equal angles (vertically - opposite angles are equal and the other given angles are equal), by the AA (Angle - Angle) similarity criterion, the triangles are similar.

Step2: Set up proportion for \(y\)

For similar triangles, the ratios of corresponding sides are equal. We have the proportion \(\frac{12}{20}=\frac{15}{y}\) (corresponding sides).
Cross - multiply: \(12y = 15\times20\)
\(12y=300\)
Solve for \(y\): \(y=\frac{300}{12}=25\)

Answer:

A. The value of \(x\) is \(21\)
A. The value of \(y\) is \(25\)