We have three points.
a = (-1,2)
b = (2,3)
c = (0,0)
These form a triangle were we want to find the angles. One way to solve the problem could be to use the law of cosines, but since you're talking about vector I assume you're supposed to use the following relationship (which is derived using the law of cosines)
u*v = |u||v|cos(θ) (were * denotes the dot product)
Now we could treat a and b as vectors from the origin to the point a, respectively. Therefore we have
a*b = |a||b|cos(θ) => -1*2+2*3 = sqrt((-1)^2+2^2)*sqrt(2^2+3^2)*cos(θ)
Try now and come back if you still don't get the idea.