[tex]m(\angle ABC)+m(\angle ACB)=180^{\circ}-45^{\circ}=135^{\circ}[/tex]
[tex]m(\angle IBC)+m(\angle ICB)=\frac{m(\angle ABC)}{2}+\frac{m(\angle ACB)}{2}=\frac{135^{\circ}}{2}[/tex]
[tex]m(\angle BIC)=180^{\circ}-\frac{135^{\circ}}{2}=\frac{360^{\circ}}{2}-\frac{135^{\circ}}{2}=\frac{225^{\circ}}{2}=112^{\circ}30'[/tex]