The right angle mark indicates that $\displaystyle\angle{A}{B}{D}\usepackage{cmbright}\Huge\$ measures $\displaystyle{{90}}^{\circ}\usepackage{cmbright}\Huge\$ . Because $\displaystyle\angle{A}{B}{C}\usepackage{cmbright}\Huge\$ is a straight angle, it measures $\displaystyle{{180}}^{\circ}\usepackage{cmbright}\Huge\$ . Therefore, $\displaystyle{{90}}^{\circ}+{m}\angle{D}{B}{C}={{180}}^{\circ}\usepackage{cmbright}\Huge\$ . It follows that $\displaystyle{m}\angle{D}{B}{C}={{90}}^{\circ}\usepackage{cmbright}\Huge\$ .