Question

use the diagram to answer questions 4 - 6:

1. name the angles adjacent to ∠xoy

1. find m∠voz
2. determine if ∠xoy and ∠wov are a linear pair, vertical angles, neither. how do you know?

Explanation:

Step1: Recall adjacent - angle definition

Adjacent angles share a common side and a common vertex. For $\angle XOY$, the adjacent angles are $\angle WOY$ and $\angle ZOX$.

Step2: Find $\angle VOZ$

We know that the sum of angles around a point is $360^{\circ}$. If we assume the angles are part of a full - circle setup and we know some of the angles. But from the diagram, we can see that $\angle VOZ = 60^{\circ}$ directly from the given angle measure.

Step3: Analyze $\angle XOY$ and $\angle WOV$

A linear pair of angles are adjacent and their sum is $180^{\circ}$. Vertical angles are non - adjacent and are formed by two intersecting lines and are equal. $\angle XOY$ and $\angle WOV$ are non - adjacent. They are vertical angles because they are formed by the intersection of two lines (the lines containing the rays that form the angles) and they are equal in measure.

Answer:

1. $\angle WOY$, $\angle ZOX$
2. $60^{\circ}$
3. Vertical angles. They are non - adjacent and formed by two intersecting lines.