To find the measure of the missing angle, let's analyze the given diagram step by step:

1. The given angle $\angle LKM = 60^\circ$.
2. $\angle LJK$ is a right angle ($90^\circ$), meaning $\angle LKM$ and $\angle MKJ$ must sum up to $90^\circ$ because they are complementary.
3. Therefore, we can find $\angle MKJ$ as: $\angle MKJ = 90^\circ - 60^\circ = 30^\circ$

So, the missing angle $\angle MKJ$ is 30 degrees.

Would you like further clarification or additional details?

Related Questions:

1. How do we classify angles based on their measurements?
2. What is the sum of angles in a triangle?
3. How do we determine an angle when given complementary or supplementary angles?
4. Can we find missing angles using trigonometry in a right triangle?
5. How do perpendicular lines affect angle calculations?

Tip:

In any right-angled triangle, the two non-right angles always add up to $90^\circ$, which helps in quick calculations.