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

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 ...

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)