Comparing angles

First note that $\angle A = \arctan \dfrac{1}{3}, \angle B = \arctan \dfrac{1}{2}$ and $\angle C = \arctan 1 = 45^{\circ}$ .

Now by the arctan sum formula $\arctan x + \arctan y = \arctan \dfrac{x + y}{1 - xy}$ we have that

$\angle A + \angle B = \arctan \dfrac{1}{3} + \arctan \dfrac{1}{2} = \arctan \dfrac{\frac{1}{3} + \frac{1}{2}}{1 - \frac{1}{3} \times \frac{1}{2}} = \arctan \dfrac{\frac{5}{6}}{\frac{5}{6}} = \arctan 1 = \angle C$ .

Thus the correct option is $\boxed{\angle A + \angle B = \angle C}$ .