Grade 12 2014 Problem 5

Neka je $ABCD$ konveksni četverokut takav da vrijedi

$$\measuredangle BAD = 90^\circ, \quad \measuredangle BAC = 2\measuredangle BDC \quad \text{i} \quad \measuredangle DBA + \measuredangle DCB = 180^\circ.$$

Odredi mjeru kuta $\measuredangle DBA$.