Question

identify two angles that are marked congruent to each other on the diagram below. (diagram is not to scale.) ∠ is congruent to ∠

Explanation:

Step1: Analyze angle markings

In the diagram, $\angle V$ and $\angle W$ have the same arc marking (curved angle mark), indicating they are congruent. Also, since $VP \perp NQ$ and $UO$ is parallel to $VP$ (from the diagram's structure with equal - length tick marks on the transversal and right angles), the corresponding angles or the marked angles $\angle V$ and $\angle W$ (or also $\angle V$ and $\angle PWR$ etc., but the most direct from the arc marks) are congruent. A common pair is $\angle UVW$ (or $\angle V$) and $\angle PWR$ (or $\angle W$), but looking at the arc marks on $\angle V$ (at vertex $V$) and $\angle W$ (at vertex $W$), these two angles are marked with the same arc, so they are congruent.

Step2: Identify the angles

From the diagram, the angle at $V$ (let's call it $\angle UVW$ or $\angle V$) and the angle at $W$ (let's call it $\angle PWR$ or $\angle W$) have the same marking, so they are congruent. A typical pair is $\angle V$ (or $\angle UVW$) and $\angle W$ (or $\angle PWR$), but more precisely, $\angle UVV$ (wait, no, the vertices: $V$ is between $U$ and $W$, $W$ is between $V$ and $R$. The angles with the arc marks are $\angle UVW$ (at $V$) and $\angle PWR$ (at $W$), but also, since $VP$ and $UO$ are perpendicular - like (or with the same angle marking), another way: the angle at $V$ ( $\angle OVW$? No, better to see the arc. The two angles with the curved mark: $\angle UVW$ (at $V$) and $\angle PWR$ (at $W$) are congruent. But also, if we consider the right angle at $P$, but the arc marks are on $\angle V$ and $\angle W$. So a correct pair is $\angle UVW$ (or $\angle V$) and $\angle PWR$ (or $\angle W$), but in the diagram, the angles with the same arc are $\angle V$ (at vertex $V$) and $\angle W$ (at vertex $W$), so we can say $\angle UVW$ is congruent to $\angle PWR$, or more simply, $\angle V$ is congruent to $\angle W$. But let's check the diagram again: the angle at $V$ (between $UV$ and $VW$) and the angle at $W$ (between $VW$ and $WR$) have the same arc, so they are congruent. Also, since $UO \parallel VP$ (from the equal tick marks on the transversal $UR$) and $VP \perp NQ$, $UO \perp NQ$ as well. But the key is the arc marking. So a valid pair is $\angle UVW$ (or $\angle V$) and $\angle PWR$ (or $\angle W$), but a common answer is $\angle V$ ( $\angle UVW$ ) and $\angle W$ ( $\angle PWR$ ), or also, if we consider the right angle, but no, the arc is not a right angle mark. Wait, the right angle is at $P$ ( $\angle VPQ$ is a right angle). The angles with the arc: $\angle UVW$ and $\angle PWR$ are congruent. So we can write $\angle UVW$ is congruent to $\angle PWR$, or using the vertex labels, $\angle V$ (at $V$) and $\angle W$ (at $W$).

Answer:

$\angle UVW$ is congruent to $\angle PWR$ (or $\angle V$ is congruent to $\angle W$)