All angle in a triangle add up to 180 degrees. Since we know two so far we can solve for the third.
angle 1 = 180 - 55 - 40 = 85 degrees.
From the hash marks we can tell that each length in the smaller triangle is half the side lengths of the larger triangle. This means all the angle in the larger triangle will match the angle in the smaller triangle. So <KKL = 40 and <JLK = 85.
The length of MN will be 1/2 the length of KL so MN = 1/2(30) = 15
MK = 1/2 JK and JK = 20 thus MK = 10 since 10 is half of 20.
JL = twice the length from J to N. We know JN = 14 so that means JL must be 28.