Question

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

Explanation:

Step1: Find the third angle of $\triangle RST$

The sum of angles in a triangle is $180^{\circ}$. For $\triangle RST$, let the third angle be $\angle S$. Then $\angle S=180^{\circ}-(43^{\circ} + 55^{\circ})=180^{\circ}-98^{\circ}=82^{\circ}$.

Step2: Compare angles of $\triangle RST$ and $\triangle TUV$

In $\triangle RST$, angles are $43^{\circ},55^{\circ},82^{\circ}$. In $\triangle TUV$, angles are $82^{\circ},55^{\circ},(180^{\circ}-(82^{\circ}+55^{\circ})) = 43^{\circ}$ (using the angle - sum property of a triangle).
Since all three pairs of corresponding angles are equal, 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), $\triangle RST\sim\triangle TUV$.

Answer:

$\triangle RST$ is similar to $\triangle TUV$.