Question

identify the second step of constructing congruent angles.

with the pointed end of the compass on vertex x, draw an arc that intersects the sides of ∠x. label the points of intersection as z and y.

draw a ray with endpoint l.

with the same compass setting, place the pointed end of the compass on point l. draw an arc and label its point of intersection with the ray as m.

set the compass to have the length of yz. with same compass setting, place the pointed end of the compass on m and draw an arc to locate the point n.

Explanation:

Step1: Recall steps for constructing congruent angles.

The first step is usually drawing a ray (e.g., with endpoint \( L \)), then the second step involves working with the original angle. The standard steps for constructing a congruent angle to \( \angle X \) are: 1. Draw a ray with endpoint \( L \). 2. With compass on \( X \), draw arc intersecting sides at \( Y, Z \). Wait, no—wait, let's re - order. Wait, actually, the correct order of steps for constructing a congruent angle:

1. Draw a ray (let's say with endpoint \( L \)) – this is the first step to create the base of the new angle.
2. Then, on the original angle \( \angle X \), place the compass on \( X \), draw an arc intersecting the two sides at \( Y \) and \( Z \).

Wait, but let's check the options. The options are:

Option 1: With the pointed end of the compass on vertex \( X \), draw an arc that intersects the sides of \( \angle X \). Label the points of intersection as \( Z \) and \( Y \).

Option 2: Draw a ray with endpoint \( L \). (This is step 1)

Option 3: With the same compass setting, place the pointed end of the compass on point \( L \). Draw an arc and label its point of intersection with the ray as \( M \). (This is step 3 or later)

Option 4: Set the compass to have the length of \( YZ \). With same compass setting, place the pointed end of the compass on \( M \) and draw an arc to locate the point \( N \). (This is step 4 or later)

So the first step is drawing the ray (option 2), then the second step is working on the original angle: placing compass on \( X \), drawing arc intersecting sides at \( Y, Z \) (option 1).

Step2: Match the step number.

Since the first step is drawing the ray (option 2), the second step should be the one that deals with the original angle \( \angle X \), which is the first option: "With the pointed end of the compass on vertex \( X \), draw an arc that intersects the sides of \( \angle X \). Label the points of intersection as \( Z \) and \( Y \)."

Answer:

The correct option is: With the pointed end of the compass on vertex \( X \), draw an arc that intersects the sides of \( \angle X \). Label the points of intersection as \( Z \) and \( Y \). (The first option in the list of choices)