Question

which angles are vertical angles? image of intersecting lines with points t, u, v, s, w, x, y, z options: ∠tux and ∠tus, ∠tux and ∠wxu, ∠tus and ∠wxz, ∠yxu and ∠wxz

Explanation:

Step1: Recall Vertical Angles Definition

Vertical angles are formed by two intersecting lines and are opposite each other, sharing a common vertex but no common side.

Step2: Analyze Each Option

• Option 1: $\angle TUX$ and $\angle TUS$ share a common side (TU) and vertex (U), so they are adjacent, not vertical.
• Option 2: $\angle TUX$ and $\angle WXU$: Lines TV and WY are parallel, and line SZ intersects them. But these angles are same - side or alternate? Wait, no, let's check vertices. $\angle TUX$ has vertex U, $\angle WXU$ has vertex X? No, wait, no, looking at the diagram, U and X are intersection points. Wait, no, re - examine: Wait, the correct vertical angles should be formed by two intersecting lines. Wait, line SZ intersects TV at U and WY at X. Wait, no, the angles $\angle YXU$ and $\angle WXZ$: Wait, no, let's check the last option: $\angle YXU$ and $\angle WXZ$. When two lines (SZ and WY) intersect? Wait, no, SZ intersects TV at U and WY at X. Wait, actually, $\angle TUS$ and $\angle WXZ$: No, wait, the correct pair is $\angle YXU$ and $\angle WXZ$. Wait, let's re - do:

Wait, vertical angles are opposite when two lines cross. So when line SZ intersects line WY at X, the vertical angles are $\angle YXU$ and $\angle WXZ$ (since they are opposite each other at the intersection of SZ and WY). Let's check each option again:

• $\angle TUX$ and $\angle TUS$: Adjacent, share side TU.
• $\angle TUX$ and $\angle WXU$: These are same - side interior angles (since TV || WY and SZ is transversal), not vertical.
• $\angle TUS$ and $\angle WXZ$: $\angle TUS$ is at U, $\angle WXZ$ is at X, different vertices, not vertical.
• $\angle YXU$ and $\angle WXZ$: These are formed by the intersection of SZ and WY, opposite each other, so they are vertical angles.

Answer:

$\angle YXU$ and $\angle WXZ$