Divide into 2 isosceles triangles
Python 3.8 (pre-release), 123 129 bytes

g=lambda*p:[[180-2*x,x]for x in p]
f=lambda a,b:((c:=180-a-b)==90or c&gt;45&gt;2in{a/b,b/a})*g(a,b)or(c/3in{a,b})*g(c/3,c/3*2)or f(b,c)

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A function that takes in 2 angles, and returns the 2 isosceles triangles. If the given triangle cannot be divided, the function loops forever.