Question

which angles are adjacent to each other? select all that apply.
(image of intersecting lines with angles labeled 1,2,3,4,5,6)
options: ∠5 and ∠6, ∠6 and ∠2, ∠5 and ∠2, ∠4 and ∠6

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 pair

• For $\angle5$ and $\angle6$: They share a common side (the middle ray) and a common vertex, so they are adjacent.
• For $\angle6$ and $\angle2$: They share a common side (the left - most ray) and a common vertex, so they are adjacent.
• For $\angle5$ and $\angle2$: $\angle5$ and $\angle2$ do not share a common side. The sides of $\angle5$ are the middle ray and the right - most ray, and the sides of $\angle2$ are the left - most ray and the ray between $\angle2$ and $\angle1$. So they are not adjacent.
• For $\angle4$ and $\angle6$: They share a common side (the middle ray) and a common vertex, so they are adjacent.

Answer:

$\angle5$ and $\angle6$, $\angle6$ and $\angle2$, $\angle4$ and $\angle6$