Answer:
34
Step-by-step explanation:
Inscribed angles
Recall inscribed angles. If two chords are drawn from two points on the circumference of a circle, and they connect at a different point on the circumference, then an inscribed angle is created. The inscribed angle is half the measure of the arc between its endpoints.
Finding K's measure
In this case, K is the inscribed angle made from the chords of J and I. Noticing that JI is the diameter of the circle, the arc length of JI is half of the circle's circumference. If the arc length is half the circle's circumference then the arc measure is half of the circle's measure or 180 degrees. This makes angle K 90 degrees.
Why was find K important?
Finding K can help us find the measure of J since points J,K, and I create a triangle. A triangle always has an angle sum of 180 degrees, if we already know the measure of K and I, all there's left is the subtract those measures from 180 to find J's measure!
`180 - K - I = J
180 - 90 - 56 = 34 = J
