Some steps to construct an angle MNT congruent to angle PQR are listed below. Step 1: Draw a segment NT.
Step 2: Use a compass to draw an arc from point Q that intersects the side PQ of angle PQR at point A and the side QR at point B.
Step 3:
Step 4: Adjust the width of the compass to AB, and draw an arc from point X such that it intersects the arc drawn from N in a point Y.
Step 5: Join points N and Y using a straightedge.

Which statement describes step 3 correctly?

Use the same width of the compass to draw an arc from point T that intersects the segment NT at a point X.
Use the same width of the compass to draw an arc from point N that intersects the segment NT at a point X.
Use the same width of the compass to draw an arc from point A that intersects the segment NT at a point X.
Use the same width of the compass to draw an arc from point B that intersects the segment NT at a point X.

Use the same width of the compass to draw an arc from point N that intersects the segment NT at a point X.

This option gives us the step 3.

This is because we want to have equal angles. Therefore we select an arc equal in length to arc AB which intersects NT at  point X.

This can be explained more with the help of a diagram.

Two angles are equal when their dimensions are equal.

Arcs of equal length would give congruent angles.

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From the description of the construction of the congruent angle, we have;

The statement that describes step 3 correctly is; Use the same width of the compass to draw an arc from point N that intersects the segment AN at a point X

The reason for making the above selection is as follows:

The steps to construct an angle congruent to another angle are;

Step 1: Given an angle PQR, draw a working segment NT

Step 2: Place the needle of the compass at point Q and draw an arc (Q, QA), intersecting sides PQ and QR of the angle ∠PQR at points A and B respectively

Step 3: Place the needle of the compass at point N and draw an arc with the compass width QA from above the to intersect the segment NT at a point X

Step 4: Set the compass width to the distance AB with which an arc is drawn from point X so as to intersect the arc (N, QA) above at point Y

Step 5: The points Y and N are joined with a straight line to form the congruent angle

Analysis of the steps:

Given that in step 4, we have that the the arc drawn from point X with compass width AB is meant to intersect the arc drawn from point N, at point Y, we have that in step 3 an arc was drawn from point N with compass width QA from step 2 to intersect NT at a point X

Therefore;

Step 3 is best described by the following statement;

Use the same width of the compass to draw an arc from point N that intersects the segment AN at a point X

Learn more about the construction of congruent angles here:

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