Final answer:
To find mLMK, use the fact that the sum of the measures of the angles in a triangle is 180 degrees.
Step-by-step explanation:
In the given diagram, we are given that mJK = 20 and mJL = 55. We need to find mLMK. In a triangle, the sum of the measures of the angles is 180 degrees. Therefore, mL + mK + mLMK = 180. Substituting the given values, we get 55 + 20 + mLMK = 180. Solving for mLMK, we find mLMK = 105 degrees.