Question

Is a triangle with two congruent sides always have 45 45 and 90 degrees?

Answer 1

No.  Two angles will have to be the same and the third angle will just be 180° minus twice the smaller angles.

So if we let the equal angles equal a, and the large angle equal be we have:

2a+b=180

So there are infinitely many values that a and b can have.

a=(180-b)/2, so the smaller equal angles have the range (0,90)

b=180-2a, so the larger has a range of (0,180)

Answer 2

No.
Taat triangle is right-angled ( one angle = 90 degrees)
There are many triangles with congruent sides     where 2 angles are equal and the other  is 180 - sum of these 2, for example 

30 30 120
50 50 80
40 40 100   etc...