Question

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

Explanation:

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

The sum of angles in a triangle is $180^{\circ}$. For $\triangle FGH$, if two angles are $71^{\circ}$ and $47^{\circ}$, then the third angle $\angle F=180^{\circ}-(71^{\circ} + 47^{\circ})=62^{\circ}$.

Step2: Check the angle - angle similarity criterion

In $\triangle FGH$, angles are $71^{\circ},47^{\circ},62^{\circ}$. In $\triangle IJK$, angles are $71^{\circ},62^{\circ}$. Since the sum of angles in a triangle is $180^{\circ}$, the third angle of $\triangle IJK$ is $180^{\circ}-(71^{\circ}+62^{\circ}) = 47^{\circ}$. By the AA (angle - angle) similarity criterion (if two angles of one triangle are equal to two angles of another triangle, the triangles are similar), $\triangle FGH\sim\triangle IJK$.

Answer:

$\triangle FGH$ is similar to $\triangle IJK$.