Question

solve for ( x ). round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.
answer attempt 4 out of 100
( x=)

Explanation:

Step1: Find the third angle of each triangle

For \(\triangle LMN\), the third angle \(=180^{\circ}-43^{\circ}-72^{\circ}=65^{\circ}\)
For \(\triangle QRO\), the third angle \(=180^{\circ}-65^{\circ}-43^{\circ}=72^{\circ}\)
Since the angles of \(\triangle LMN\) and \(\triangle QRO\) are equal, the two triangles are similar.

Step2: Set up the proportion

Since the triangles are similar, \(\frac{LM}{QO}=\frac{LN}{QR}\)
Substitute \(LM = 67\), \(QO = 80\), \(LN = 94\), and \(QR=x\) into the proportion: \(\frac{67}{80}=\frac{94}{x}\)
Cross - multiply: \(67x=94\times80\)
\(67x = 7520\)
Solve for \(x\): \(x=\frac{7520}{67}\approx112.2\)

Answer:

\(x\approx112.2\)