Question

drag each tile to the correct location in the table.
\overleftrightarrow{wx} and \overleftrightarrow{yz} intersect in the figure. use the figure to identify each pair of angles as adjacent or vertical.
the figure shows two intersecting lines \overleftrightarrow{wx} (horizontal) and \overleftrightarrow{yz} (diagonal), forming angles 1, 2, 3, 4 at the intersection. the angle pairs to classify are: \angle1 and \angle2, \angle1 and \angle3, \angle2 and \angle3, \angle2 and \angle4, \angle3 and \angle4, \angle4 and \angle1. there are two categories: adjacent and vertical, with empty boxes to drag the angle pairs into.

Explanation:

Adjacent angles share a common side and vertex, and form a linear pair (sum to 180°). Vertical angles are opposite each other when two lines intersect, sharing only a vertex.

1. $\angle1$ and $\angle2$: Share a side/vertex, linear pair → adjacent
2. $\angle1$ and $\angle3$: Opposite each other at intersection → vertical
3. $\angle2$ and $\angle3$: Share a side/vertex, linear pair → adjacent
4. $\angle2$ and $\angle4$: Opposite each other at intersection → vertical
5. $\angle3$ and $\angle4$: Share a side/vertex, linear pair → adjacent
6. $\angle4$ and $\angle1$: Share a side/vertex, linear pair → adjacent

Answer:

Adjacent:

$\boldsymbol{\angle1}$ and $\boldsymbol{\angle2}$, $\boldsymbol{\angle2}$ and $\boldsymbol{\angle3}$, $\boldsymbol{\angle3}$ and $\boldsymbol{\angle4}$, $\boldsymbol{\angle4}$ and $\boldsymbol{\angle1}$

Vertical:

$\boldsymbol{\angle1}$ and $\boldsymbol{\angle3}$, $\boldsymbol{\angle2}$ and $\boldsymbol{\angle4}$