Can anyone ? what are the measures of jk and angle kij?

Check the picture below.

notice, on the left-side is the "inscribed angle theorem".

so, the angle at J is an inscribed angle, with an intercepted arcKI, which happens to be 116°, and therefore the inscribed angle is half that.

and since all interior angles in a triangle add up to 180°, then the angle at I is 52°, as shown there, however, that angle is also inscribed in the circle, and intercepting arcJK, so arcJK is twice as much as that angle, as shown there.