Missing Quadrilateral Angle

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Please find the missing green angle for the quadrilateral using simple geometry and explain your steps. I am not able to use trigonometry for this problem. Thank you. enter image description here

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$ABCD$ is cyclic so the opposite angles are supplementary

$\angle BCD=130°\to \angle ACD=130°-90°=40°$

Or since it's cyclic we can use the inscribed angle. The central angle is already given as $80°$.

So $\angle ACD=\frac12\,80°=40°$ enter image description here