Question

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

Explanation:

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

The sum of angles in a triangle is $180^{\circ}$. For $\triangle ABC$, let the third angle be $\angle B$.
$$\angle B=180^{\circ}-(15^{\circ}+45^{\circ})=120^{\circ}$$

Step2: Compare angles of $\triangle ABC$ and $\triangle DEF$

In $\triangle ABC$, angles are $15^{\circ},45^{\circ},120^{\circ}$. In $\triangle DEF$, angles are (let's assume we find them in a similar way as above, but we already have $\angle E = 120^{\circ},\angle F=45^{\circ}$. Then the third angle $\angle D=180^{\circ}-(120^{\circ}+45^{\circ}) = 15^{\circ}$).
Since all corresponding angles of $\triangle ABC$ and $\triangle DEF$ are equal ($\angle A=\angle D = 15^{\circ},\angle B=\angle E=120^{\circ},\angle C=\angle F = 45^{\circ}$), by the AA (angle - angle) similarity criterion, the triangles are similar.

Answer:

$\triangle ABC$ is similar to $\triangle DEF$.