Given that A + B = C and that C is perpendicular to A. Further |A|=|C| then what is the angle between A and B?

Since C is perpendicular to A, therefore,A2 +C2 = B2But A=C. Hence C=B/2=Aso, cos⁡θ=C2−A2−B22AB=B2/2−B2/2−B22(B/2)B=−B22B2=−12θ=135∘ or (3π/4)radSee figure