Question

Find the measure of the arc on the picture. The lines are tangent. Assume they are tangent. Find missing arc

Answer 1

Angle EJM (69°) and Angle KJL(69°) will EACH equal one half of the intercepted arcs.
So, 69° = .5 * (arc EM + arc KL)
69° = .5 * (58° + arc KL)
69° = 29 + .5 *arc KL
40° = .5 * arc KL
Therefore arc KL = 80°

Source:
http://www.1728.org/circangl.htm
answer is B