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Let $G$ be a circle with the centre $O$. $G$ is inside the quadrilateral $ABCD$ where the angles for $A, B,C$ and $D$ is 105, 94, 76 and 85. $G$ is a tangent to the sides $AB;BC;CD;DA$ in the points $X;Y;Z;T$. How do you determine the angles $∠XOY; ∠YOZ; ∠ZOT$ and $∠TOX$?

It seems like we got a Tangential quadrilateral and I can find a lot of properties where I can find here but I struggle to see what angle formula to use.

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Hint: The angles at $X$ and $Y$ will be $90^{\circ}$ and the angles in a quadrilateral add upto ... ?

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