The measure of [tex]\angle BAD[/tex] is required.
The required angle is [tex]110^{\circ}[/tex]
The given angles are
[tex]\angle ABC=85^{\circ}[/tex]
[tex]\angle BCA=25^{\circ}[/tex]
As the sum of all the angles in a triangle is [tex]180^{\circ}[/tex]
[tex]\angle ABC+\angle BCA+\angle BAC=180^{\circ}\\\Rightarrow \angle BAC=180-85-25=70^{\circ}[/tex]
Angle BAD and BAC are supplementary angles so
[tex]\angle BAD+\angle BAC=180\\\Rightarrow \angle BAD=180-70\\\Rightarrow \angle BAD=110^{\circ}[/tex]
The required angle is [tex]110^{\circ}[/tex]
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