How to proof that those triangles are similar?

Question

I have given that :

The triangle ABC Isosceles triangle(AC = BC)
The angle at the base is 72 degrees
There is a bisector L for the angle A

I have to proof that the triangle ABC is similar to the triangle BLA

So far I have found that:

The angles of the triangle ABC are :
angle A = 72 degrees (by definition)
Angle B = 72 degrees (by definition)
Angle C = 180 - 2*72 = 180 - 144 = 36 degrees
The angles of the triangle BLA are:
Angle A = 31 degrees(since L is bisector for the angle A)
Angle B = 72 degrees (by definition)
Angle L = 180 - (31+72) = 180 - 101 = 79 degrees

Now since, the tutorial is about the first sign similarity(if two triangles have 2 angles that are the same(angle A = angle A1, angle B = angle B1), the triangles are similar). I assume that I have to proof it this way, but I can't find two angles that are the same. I'm not sure about angle A in triangle BLA, I think it should be 31 degrees but I think I'm wrong.

Answer 1

Angle $A$ is $\frac{72}{2}=36$ not $31$.