Question

name the marked angle in 2 different ways.

Explanation:

Step1: Identify the vertex and sides

The marked angle has vertex U, with sides UV and UT (or also US? Wait, looking at the diagram, the points are V, U, T, S. So the angle at U is between VU and TU, or also between VU and SU? Wait, the diagram: V connected to U, U connected to T, T connected to S, S connected to V? Wait, no, the diagram shows V at top, S at bottom left, T at bottom right, U at right. So the angle at U is between VU (from U to V) and TU (from U to T), or also can be named by the vertex alone if it's the only angle at U. Wait, no, the standard ways to name an angle: 1) using three points with the vertex in the middle, 2) using the vertex alone if there's only one angle at that vertex.

So first way: using three points, the angle is ∠VUT (since vertex is U, and the sides are UV and UT, so the points are V, U, T with U in the middle). Second way: using the vertex, ∠U (since it's the only angle marked at U, so we can name it by the vertex).

Wait, let's confirm. The angle is at U, between UV and UT (or UV and US? Wait, S is connected to T and V? Wait, the diagram: V---U, U---T, T---S, S---V? So it's a quadrilateral VUTS? So the angle at U is between VU and TU (since V to U to T, and U to S? Wait, no, the marked angle is the pink one at U, between VU and TU? Wait, the sides of the angle: one side is from U to V, the other is from U to T (or U to S? Wait, S is connected to T and V. Wait, maybe the angle is between VU and SU? No, the pink angle is at U, so let's see the points: V, U, T, S. So the angle at U is formed by segments VU and TU (or VU and SU? Wait, maybe the diagram is a quadrilateral with vertices V, S, T, U? Wait, V connected to S, S connected to T, T connected to U, U connected to V? Then the angle at U is between VU and TU. So the three-point name is ∠VUT (vertex U, with V and T as the other two points), and the single-vertex name is ∠U (since there's only one angle marked at U).

So first way: ∠U (using the vertex), second way: ∠VUT (using three points with U in the middle).

Step2: Verify the angle naming rules

Angle naming: 1) By vertex: if only one angle at the vertex, we can name it ∠U. 2) By three points: the middle letter is the vertex, so ∠VUT (V - U - T, with U as vertex).

Answer:

$\angle U$; $\angle VUT$