Question

triangle lmn has two known interior angles of 29° and 104°. triangle jkl has two known interior angles of 57° and 104°. what can be determined about whether triangles lmn and jkl are similar? the triangles are similar. the triangles are not similar. similarity cannot be determined from the given information. all interior angles must be given to determine similarity.

Explanation:

Step1: Calculate the third angle of triangle LMN

The sum of interior angles of a triangle is \(180^{\circ}\). Let the third angle of \(\triangle LMN\) be \(x\). Then \(x = 180^{\circ}-(29^{\circ}+ 104^{\circ})=180^{\circ}-133^{\circ}=47^{\circ}\)

Step2: Calculate the third angle of triangle JKL

Let the third angle of \(\triangle JKL\) be \(y\). Then \(y = 180^{\circ}-(57^{\circ}+104^{\circ})=180^{\circ}-161^{\circ}=19^{\circ}\)

Step3: Check for similarity

For two triangles to be similar, their corresponding angles must be equal. \(\triangle LMN\) has angles \(29^{\circ},104^{\circ},47^{\circ}\) and \(\triangle JKL\) has angles \(57^{\circ},104^{\circ},19^{\circ}\). Only one angle (\(104^{\circ}\)) is common.

Answer:

The triangles are not similar.