Question

Quadrilateral DUCK is inscribed in circle O what is the measure of

Answer 1

95 degrees

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!

Answer 2

95°

Explanation:

Since, quadrilateral DUCK is inscribed in circle O

sum of the opposite angles of the quadrilateral is 180°

m<K +m<U= 180°

m<K= 180°- 85°= 95°