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 24
(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: Determine similarity of triangles

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

Step2: Use the property of similar triangles (proportional sides)

For similar triangles, the ratios of corresponding sides are equal.
We have \(\frac{x}{24}=\frac{18}{18}\) (from the first pair of corresponding sides). But a more general proportion for finding \(y\) is \(\frac{15}{y}=\frac{18}{33}\) (cross - multiply)

$$18y = 15\times33$$

$$y=\frac{15\times33}{18}=\frac{495}{18} = 27.5$$

Answer:

A. The value of \(x\) is \(24\).
A. The value of \(y\) is \(27.5\)