Answer :
Based on the given diagram, the measure of the arc can be computed using the definition of a circle. One complete revolution of a circle is equal to 360 degrees. If given that we have the arc LJ equal to 240 degrees, the remaining arc, let as x, can be computed as
[tex]x+240=360[/tex]Solve for the value of x, we get
[tex]x=360-240=120[/tex]Finally, to solve for the angle K, we just divide the solved arc measure by half of it, getting
[tex]m\angle K=\frac{120}{2}=60[/tex]Hence, the measure of angle K is 60 degrees while the measure of the arc that corresponds to angle K is 120 degrees.