The drawing indicates that $\displaystyle\angle{B}{D}{C}\usepackage{cmbright}\Huge\$ measures $\displaystyle{{80}}^{\circ}\usepackage{cmbright}\Huge\$ . Because $\displaystyle\angle{A}{D}{C}\usepackage{cmbright}\Huge\$ is a straight angle, it measures $\displaystyle{{180}}^{\circ}\usepackage{cmbright}\Huge\$ . Therefore, $\displaystyle{{80}}^{\circ}+{m}\angle{D}{B}{C}={{180}}^{\circ}.\usepackage{cmbright}\Huge\$ It follows that $\displaystyle{m}\angle{D}{B}{C}={{100}}^{\circ}.\usepackage{cmbright}\Huge\$