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 180^o]

(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,

\[\angle ADC\text{ }=\text{ }{{75}^{o}}\]