Question

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wx and yz intersect in the figure. use the figure to identify each pair of angles as adjacent or vertical.

adjacent \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tvertical

Explanation:

To determine if angles are adjacent or vertical, we use the definitions:

• Adjacent Angles: Share a common side and vertex, and their non - common sides form a linear pair (or they are next to each other).
• Vertical Angles: Opposite angles formed by the intersection of two lines, they are equal in measure and share a common vertex but no common side.

Step 1: Analyze $\angle1$ and $\angle2$

$\angle1$ and $\angle2$ share a common vertex and a common side. Their non - common sides form a straight line (since $WX$ is a straight line). So, they are adjacent.

Step 2: Analyze $\angle1$ and $\angle3$

$\angle1$ and $\angle3$ are opposite angles formed by the intersection of lines $WX$ and $YZ$. They share a common vertex but no common side. So, they are vertical.

Step 3: Analyze $\angle2$ and $\angle3$

$\angle2$ and $\angle3$ share a common vertex and a common side. Their non - common sides form a straight line (since $YZ$ is a straight line). So, they are adjacent.

Step 4: Analyze $\angle2$ and $\angle4$

$\angle2$ and $\angle4$ are opposite angles formed by the intersection of lines $WX$ and $YZ$. They share a common vertex but no common side. So, they are vertical.

Step 5: Analyze $\angle3$ and $\angle4$

$\angle3$ and $\angle4$ share a common vertex and a common side. Their non - common sides form a straight line (since $WX$ is a straight line). So, they are adjacent.

Step 6: Analyze $\angle4$ and $\angle1$

$\angle4$ and $\angle1$ share a common vertex and a common side. Their non - common sides form a straight line (since $YZ$ is a straight line). So, they are adjacent.

Answer:

Adjacent Angles:

$\angle1$ and $\angle2$, $\angle2$ and $\angle3$, $\angle3$ and $\angle4$, $\angle4$ and $\angle1$

Vertical Angles:

$\angle1$ and $\angle3$, $\angle2$ and $\angle4$