Question

k m n 20° o 122° p which statement is true? δklm is similar to δnop. δklm is not similar to δnop. there is not enough information to determine whether the triangles are similar.

Explanation:

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

The sum of angles in a triangle is $180^{\circ}$. For $\triangle KLM$, let the third angle be $\angle K$. Then $\angle K=180^{\circ}-(122^{\circ} + 38^{\circ})=180^{\circ}-160^{\circ}=20^{\circ}$.

Step2: Check the angle - angle similarity criterion

In $\triangle KLM$, angles are $122^{\circ},38^{\circ},20^{\circ}$. In $\triangle NOP$, angles are $122^{\circ},20^{\circ}$. Let the third angle of $\triangle NOP$ be $\angle P$. Using the angle - sum property of a triangle ($\angle N+\angle O+\angle P = 180^{\circ}$), we have $\angle P=180^{\circ}-(122^{\circ}+20^{\circ}) = 38^{\circ}$.
Since the three angles of $\triangle KLM$ ($122^{\circ},38^{\circ},20^{\circ}$) are equal to the three angles of $\triangle NOP$ ($122^{\circ},38^{\circ},20^{\circ}$) respectively, by the AA (angle - angle) similarity criterion (if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar), $\triangle KLM\sim\triangle NOP$.

Answer:

$\triangle KLM$ is similar to $\triangle NOP$.