Question

△lmn and △opq are shown below. which statement is true? △lmn is similar to △opq. △lmn is not similar to △opq. there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Calculate the third angle of $\triangle LMN$

The sum of angles in a triangle is $180^{\circ}$. For $\triangle LMN$, if two angles are $57^{\circ}$ and $61^{\circ}$, then the third angle $\angle N=180^{\circ}-(57^{\circ} + 61^{\circ})=180^{\circ}-118^{\circ}=62^{\circ}$.

Step2: Check for similarity using AA (Angle - Angle) criterion

In $\triangle LMN$, angles are $57^{\circ},61^{\circ},62^{\circ}$. In $\triangle OPQ$, angles are $57^{\circ},62^{\circ}$ (given). Since two pairs of angles are equal ($\angle L=\angle O = 57^{\circ}$ and $\angle N=\angle Q=62^{\circ}$), by AA (Angle - Angle) similarity criterion, $\triangle LMN\sim\triangle OPQ$.

Answer:

$\triangle LMN$ is similar to $\triangle OPQ$.