If A+B=C and A=B=C then what should be the angle between A and B ?

Given,

$A+B=C, \quad A=B=C$

Let, $|A|=|B|=|C|=P$

Vector addition,

$\begin{array}{l} A+B=C \\ \Rightarrow|C|^{2}=|A|^{2}+|B|^{2}+2|A||B| \\ \cos \theta \\ \Rightarrow P^{2}+P^{2}+2 \cdot P \cdot P \cdot \cos \theta=P^{2} \\ \Rightarrow 2 P^{2} \cos \theta=-P^{2} \\ \Rightarrow \cos \theta=-\frac{1}{2} \\ \Rightarrow \theta=120^{\circ} \\ \Rightarrow \theta=\frac{2 \pi}{3} \end{array}$

Answen: $\frac{2 \pi}{3}$.