You can only draw one unique isosceles triangle that contains an angle of 55°?

You can actually draw a lot! Imagine that the isosceles triangle has one angle of 55 degrees, and then the other two are the same (62.5 degrees, which adds up to 180). Or you could draw an isosceles with two 55 degree angle, and one 70 degree angle (again, to add up to 180). 

None of the options you showed are it.

Need to see the diagram