Question

select the statements that are true. ∠x and ∠z are vertical angles. ∠a and ∠b are vertical angles. ∠x and ∠y are vertical angles. ∠d and ∠b are vertical angles.

Explanation:

Vertical angles are pairs of opposite, non-adjacent angles formed by intersecting lines.

1. $\angle x$ and $\angle z$: These are opposite each other at the intersection of two lines, so they are vertical angles.
2. $\angle a$ and $\angle b$: These are adjacent angles (share a side) formed by intersecting lines, not vertical angles.
3. $\angle x$ and $\angle y$: These are adjacent angles (share a side) formed by intersecting lines, not vertical angles.
4. $\angle d$ and $\angle b$: These are opposite each other at the intersection of two lines, so they are vertical angles.

Answer:

$\boldsymbol{\angle x}$ and $\boldsymbol{\angle z}$ are vertical angles.
$\boldsymbol{\angle d}$ and $\boldsymbol{\angle b}$ are vertical angles.