Question

solve for x. round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.
answer attempt 2 out of 2
x = submit answer

Explanation:

Step1: Identify similar triangles

Since the angles of triangle \(KIJ\) (\(75^{\circ},55^{\circ},50^{\circ}\)) and triangle \(NML\) (\(75^{\circ},55^{\circ},50^{\circ}\)) are equal, the two triangles are similar by the AA (Angle - Angle) similarity criterion.

Step2: Set up proportion

For similar triangles, the ratios of corresponding sides are equal.
\(\frac{KI}{NM}=\frac{IJ}{ML}\)
We know \(KI = 15\), \(IJ=14\), \(ML = 20\), and \(NM=x\)
The proportion becomes \(\frac{15}{x}=\frac{14}{20}\)

Step3: Solve for \(x\)

Cross - multiply: \(14x=15\times20\)
\(14x = 300\)
\(x=\frac{300}{14}\approx21.4\)

Answer:

\(21.4\)