To know if 2 triangles are similar, we would need at least 2 angles, why?
Since a triangle has 3 angles, and those angles add up to 180°, we can easily determine the third angle.
Example: If 2 angles of a triangle were 13 and 97, we would know that 13 + 97 = 110, then 180° - 110° = 70°, so the missing angle is worth 70°.
Hope this helped! c: