Question

solve for x. round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.

Explanation:

Step1: Determine similarity of triangles

Since \(\angle K = \angle N=75^{\circ}\), \(\angle I=\angle L = 50^{\circ}\), \(\angle J=\angle M = 55^{\circ}\), by the AA (Angle - Angle) similarity criterion, \(\triangle KIJ\sim\triangle NML\).

Step2: Set up proportion

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

Step3: Solve for \(x\)

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

Answer:

\(x\approx21.4\)