Question

select all the pairs of adjacent angles.
∠stw and ∠vwy ∠stw and ∠str
∠xwt and ∠str ∠vwt and ∠xwt

Explanation:

Step1: Recall adjacent angles definition

Adjacent angles share a common side and vertex, and their non - common sides are distinct rays.

Step2: Analyze each pair

• For $\angle STW$ and $\angle STR$: They share vertex $T$ and common side $ST$, non - common sides $TW$ and $TR$ are distinct. So they are adjacent.
• For $\angle VW T$ and $\angle XWT$: They share vertex $W$ and common side $WT$, non - common sides $VW$ and $XW$ are distinct. So they are adjacent.
• For $\angle STW$ and $\angle VWY$: These two angles do not share a common side or vertex (vertex $T$ and $W$ are different), so they are not adjacent.
• For $\angle XWT$ and $\angle STR$: These two angles do not share a common side or vertex (vertex $W$ and $T$ are different), so they are not adjacent.

Answer:

$\angle STW$ and $\angle STR$, $\angle VW T$ and $\angle XWT$