Solution:
According to the given question, it’s clear that
In cyclic quadrilateral \[ABCD,\text{ }DC\text{ }||\text{ }AB\]
And given, \[\angle DAB\text{ }=\text{ }{{105}^{o}}\]
(i) Hence,
\[\angle BCD\text{ }=\text{ }{{180}^{o}}-\text{ }{{105}^{o}}~=\text{ }{{75}^{o}}\]
[Sum of opposite angles in a cyclic quadrilateral is 180o]
(ii) So,
\[\angle ADC\text{ }and\angle DAB\] are corresponding angles.
Thus,
\[\angle ADC\text{ }+\angle DAB\text{ }=\text{ }{{180}^{o}}\]
\[\angle ADC\text{ }=\text{ }{{180}^{o}}-\text{ }{{105}^{o}}\]
Hence,
\[\angle ADC\text{ }=\text{ }{{75}^{o}}\]