Let's put more details in the given figure:
Step 1: Let's first find x.
The total measure of a circle is 360°.
We get,
[tex]\text{ Arc LM + Arc MJ + Arc JR + x = 360}\degree[/tex][tex]\text{ 100}\degree\text{ + 72}\degree\text{ + 140}\degree\text{ + x = 360}\degree[/tex][tex]\text{ 312}\degree\text{ + x = 360}\degree[/tex]
[tex]\text{ x = 360}\degree\text{ - 312}\degree[/tex][tex]\text{ x = 48}\degree[/tex]
Step 2: Let's now find ∠K.
[tex]\text{ m\angle K = }\frac{1}{2}(Arc\text{ ML - x\rparen}[/tex][tex]\text{ = }\frac{1}{2}(72\text{ + 48\rparen = }\frac{1}{2}(120\degree)[/tex][tex]\text{ m\angle K = 60}\degree[/tex]
Therefore, the measure of ∠K is 60°
