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: Find ∠B in △ABC

The sum of angles in a triangle is $180^\circ$.
$\angle B = 180^\circ - 15^\circ - 45^\circ = 120^\circ$

Step2: Find ∠D in △DEF

The sum of angles in a triangle is $180^\circ$.
$\angle D = 180^\circ - 120^\circ - 45^\circ = 15^\circ$

Step3: Compare triangle angle sets

For △ABC: $\angle A=15^\circ$, $\angle B=120^\circ$, $\angle C=45^\circ$
For △DEF: $\angle D=15^\circ$, $\angle E=120^\circ$, $\angle F=45^\circ$
All corresponding angles are equal.

Answer:

△ABC is similar to △DEF.