Question

Quadrilateral DUCKDUCKD, U, C, K is inscribed in circle OOO. What is the measure of \angle K∠Kangle, K?

Answer 1

angle K = 95 degrees

Explanation:

180 - U = K

180 - 85 = K

Answer 2

Measure of ∠K=180-∠U

Or

Measure of ∠K=1/2m(arc DUC)

Explanation:

Given:

DUCK quadrilateral inscribed in circle with center O

To Find:

Measure angle K

Solution:

Here the Quadrilateral in inscribed in a circle with center O named as DUCK

So angle K and U are opposite to each other

We know that the angle of Quadrilateral inscribed in a circle are supplemenatry angles

Hence

∠U+∠K=180

Or The ∠K=1/2*m∠arc(DUC).

Hence depending on the given value for arc measure or angle of quadrilateral we calculate the angle K