Similar triangles, mistake or not?

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Recently I had a problem with similar triangles. The problem

Now, my teacher said that the triangles ABD and ACB are similar, but I was skeptical because I understood that the two angles of 30 degrees are congruent, but not the angle BAD (common angle). I see the two triangles like this.

Am I wrong or my teacher? Sorry if the problem is easy, but I really need to know if I'm wrong or not. Thank you for reading.