Question

which angles are adjacent angles? (image of lines and angles with options: ∠tur and ∠tuw; ∠tur and ∠srp; ∠tur and ∠vuw; ∠tur and ∠sru)

Explanation:

Step1: Recall adjacent angles definition

Adjacent angles share a common side and a common vertex, and their non - common sides are on opposite sides of the common side.

Step2: Analyze each option

• For $\angle TUR$ and $\angle TUW$: They share the common vertex $U$ and the common side $TU$. Their non - common sides $UR$ and $UW$ are on opposite sides of $TU$. So they meet the criteria of adjacent angles.
• For $\angle TUR$ and $\angle SRP$: They do not share a common vertex or a common side, so they are not adjacent.
• For $\angle TUR$ and $\angle VUW$: They do not share a common side (the sides of $\angle TUR$ are $TU$ and $UR$, the sides of $\angle VUW$ are $VU$ and $UW$), so they are not adjacent.
• For $\angle TUR$ and $\angle SRU$: They do not share a common side (the sides of $\angle TUR$ are $TU$ and $UR$, the sides of $\angle SRU$ are $SR$ and $RU$), so they are not adjacent.

Answer:

$\angle TUR$ and $\angle TUW$