A quadrilateral $ABCD$ is inscribed in a circle whose center is $O$. We know that $ \widehat{AOB}=90^\circ$, $ \widehat{BOC}= 60^\circ$, $ \widehat{COD}= 140^\circ$. Determine $\angle{A}$, $\angle{B}$, $\angle{C}$ and $\angle{D}$.
I really can't figure it out. Please help.
The triangles from the center are isoceles, it is a trivial matter to compute their two other angles. Then add these pairwise.