Since the form a linear pair, it means that we can add them to make the complete angle.
However, as we can see, the two angles to gether make a straight line, so the angles ABD and CBD are supplementary, that is, their sum is 180°:
[tex]\begin{gathered} \angle ABD+\angle CBD=180\degree \\ \angle ABD+135\degree=180\degree \\ \angle ABD=180\degree-135\degree \\ \angle ABD=45\degree \end{gathered}[/tex]
