Would this angle be name angle CUE or CUT ?

Step-by-step explanation:

We can model what both readings of this angle would be. Angle names are usually formed by taking the two lines that form to intersect this angle at a vertice, and these 3 make up the name.

Angle ∠CUT would be formed by the lines CU and UT. We can see that this is not the case, as the angle is formed by lines CU and CE.

Since they intersect at point U, that means the angle name would be CUE.

Hope this helped!