Answer:
95 degrees
Step-by-step explanation:
Quadrilaterals that are inscribed in circles are often called "cylic". Cyclic quadrilaterals have many unique properties. One of these is that opposite angles add up to 180 degrees.
Here, DUCK is a cyclic quadrilateral. "Opposite angles" are < U and < K, as well as < D and < C. So, since < U and < K are opposite angles in this inscribed quadrilateral, they add up to 180 degrees:
< U + < K = 180
We already know that < U = 85, so:
85 + < K = 180
< K = 95
Thus, < K is 95 degrees.
Hope this helps!
