Because $\displaystyle\angle{C}{D}{E}\usepackage{cmbright}\Huge\$ is a straight angle, the measures of $\displaystyle\angle{C}{D}{G}\usepackage{cmbright}\Huge\$ and $\displaystyle\angle{G}{D}{E}\usepackage{cmbright}\Huge\$ add up to $\displaystyle{{180}}^{\circ}\usepackage{cmbright}\Huge\$ . Adding up to $\displaystyle{{180}}^{\circ}\usepackage{cmbright}\Huge\$ makes these two angles supplementary.