∠KU and ∠LE are vertically opposite angles, which means that they are congruent, so that:
[tex]\angle KU=\angle LE=60º[/tex]
∠LUE and ∠LKE intersect the same arc mLE, which means that they are congruent:
[tex]\angle\text{LUE}=\angle\text{LKE}=32º[/tex]
∠KU and the vertex angle marked in blue are supplementary angles, which means that they add up to 180º:
[tex]\begin{gathered} 60+x=180º \\ x=180-60 \\ x=120º \end{gathered}[/tex]
Knowing two of the three angles of the upper triangle, you can calculate the measure of the missing one, ∠ULK:
[tex]\begin{gathered} 32+120+\angle\text{ULK}=180 \\ 152+\angle\text{ULK}=180 \\ \angle\text{ULK}=180-152 \\ \angle\text{ULK}=28º \end{gathered}[/tex]
∠ULK and ∠UEK intercept the same arc mKU, so they are congruent:
[tex]\angle\text{ULK}=\angle\text{UEK}=28º[/tex]
