Question

which angles are adjacent to each other? select all that apply.
image of intersecting lines with labeled angles 1 - 16
options: ∠5 and ∠8, ∠10 and ∠11, ∠5 and ∠6, ∠11 and ∠12

Explanation:

Step1: Recall the definition of adjacent angles

Adjacent angles are two angles that share a common side and a common vertex, and they do not overlap.

Step2: Analyze each option

• For $\angle5$ and $\angle8$: They are vertical angles (opposite each other when two lines intersect), not adjacent.
• For $\angle10$ and $\angle11$: They are formed by two different lines and do not share a common side or vertex in the required way.
• For $\angle5$ and $\angle6$: They share a common side (the line they are on) and a common vertex, so they are adjacent.
• For $\angle11$ and $\angle12$: They share a common side (the vertical line) and a common vertex, so they are adjacent.

Answer:

$\angle5$ and $\angle6$, $\angle11$ and $\angle12$