Precalculus, Chapter 6, 6.3, Section 6.3, Problem 79

You need to use the dot product to find the cosine of the angle between the vectors v and w, such that:
cos alpha = (v*w)/(|v|*|w|)
You need to evaluate the product of the vectors v and w, v = v_x*i + v_y*j, w = w_x*i + w_y*j , such that:
v*w = v_x*w_x + v_y*w_y
v*w = 1*2 + 1*(-2)
v*w = 2- 2
v*w = 0
Since the product of vectors v*w is 0, it is no need to evaluate (|v|*|w|) since cos alpha = 0.
cos alpha = 0 => alpha = pi/2
Hence, evaluating the angle between the vectors v and w, yields alpha = pi/2.