I have the following equilateral triangle:
In the following picture of the same equilateral triangle, the dotted lines are the normals to the surfaces:
Since this is an equilateral triangle, we know that the three angles are $60^\circ$. And the since the dashed lines are normal to the surfaces of the triangle, we know that the angle they make with the triangle surface is $90^\circ$. Using these two facts and some geometry, we can deduce that the angle between the left-most red arrow and the dashed line is $30^\circ$, as shown in the above image.
As you can see, I understand the process here, but I'm missing the geometry knowledge that allows one to deduce that the angle between the left-most red arrow and the dashed line is $30^\circ$. What is the geometrical reasoning here? Is it similarity of triangles? I would greatly appreciate it if people could please take the time to explain this.