Question

1. the triangles are similar. solve for x and y.

Explanation:

Step1: Determine y

Since the triangles are similar, corresponding angles are equal. The angle of \(43^\circ\) in the first triangle corresponds to \(y^\circ\) in the second triangle, so \(y = 43\).

Step2: Set up proportion for x

For similar triangles, the ratios of corresponding sides are equal. The vertical sides are \(x\) (first triangle) and \(12\) (second triangle), and the horizontal sides are \(21\) (first triangle) and \(14\) (second triangle). So, \(\frac{x}{12}=\frac{21}{14}\).

Step3: Solve for x

Simplify \(\frac{21}{14}=\frac{3}{2}\). Then, \(x = 12\times\frac{3}{2}= 18\).

Answer:

\(x = 18\), \(y = 43\)