#### Answer

$\angle ABC=135^{\circ}$

#### Work Step by Step

Since vertex $b$ measures $360^{\circ}$ and the smaller reflex angle of $\angle DBC $ measures $90^{\circ}$, the larger reflex angle of $\angle DBC$ equals $360^{\circ}-90^{\circ}=270^{\circ}$. This is bisected, meaning the resulting pieces are half that of the original. We want to find the angle measurement of one of these halves. $\frac{270}{2}^{\circ}=135^{\circ}$.