Solution:

The sum of angles in a quadrilateral is \[{{360}^{o}}\]

Thus,

\[\angle ADC\text{ }+\angle DAB\text{ }+\angle BCD\text{ }+\angle ABC\text{ }=\text{ }{{360}^{o}}\]

\[{{75}^{o~}}+\text{ }{{105}^{o}}~+\text{ }{{75}^{o}}~+\angle ABC\text{ }=\text{ }{{360}^{o}}\]

\[\angle ABC\text{ }=\text{ }{{360}^{o~}}-\text{ }{{255}^{o}}\]

Hence,

\[\angle ABC\text{ }=\text{ }{{105}^{o}}\]