Let's begin by listing out the information given to us:
[tex]\begin{gathered} |BD|\text{ bisects }|EBC|\text{ into equal parts}\Rightarrow\angle1=\angle2 \\ \angle2\text{ is supplementary with }\angle3;\angle2+\angle3=180^{\circ} \\ \therefore\angle1+\angle3=180^{\circ} \end{gathered}[/tex]
