To find the measure of the exterior angle at vertex K, we first need to determine the measure of angle K.
Since M < L = M < K, we know that angle M is smaller than angle K. Additionally, since M < J = 20, we know that angle M is 20 degrees.
Therefore, the measure of angle K is greater than 20 degrees.
Now, since the exterior angle at a vertex of a triangle is equal to the sum of the two opposite interior angles, we can calculate the measure of the exterior angle at vertex K:
Exterior angle at K = Measure of angle K + Measure of angle L
Exterior angle at K = Measure of angle K + Measure of angle M
Since we know that angle M = 20 degrees and angle K > 20 degrees, we can conclude that the measure of the exterior angle at vertex K is greater than 20 degrees.