Question

δklm and δnop are shown below.
which statement is true?
δklm is similar to δnop.
δklm is not similar to δnop.
there is not enough information to determine whethe

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: Compare angles of $\triangle KLM$ and $\triangle NOP$

In $\triangle KLM$, angles are $20^{\circ},122^{\circ},38^{\circ}$. In $\triangle NOP$, angles are $20^{\circ},122^{\circ}$. Since the sum of angles in a triangle is $180^{\circ}$, the third angle of $\triangle NOP$ is $180^{\circ}-(20^{\circ}+122^{\circ}) = 38^{\circ}$. So, all three angles of $\triangle KLM$ and $\triangle NOP$ are equal.

Answer:

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