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It appears you are presenting a list of angle labels and then asking to categorize pairs of angles based on their relationships. I will provide a brief overview of different types of angle relationships to assist you in categorizing them.

1. Alternate Interior Angles: These angles are on opposite sides of the transversal and inside the two lines. They are equal if the lines are parallel.

2. Alternate Exterior Angles: These angles are on opposite sides of the transversal and outside the two lines. They are equal if the lines are parallel.

3. Same Side Interior Angles: These angles are on the same side of the transversal and inside the two lines. They are supplementary (add up to 180 degrees) if the lines are parallel.

4. Corresponding Angles: These angles are on the same side of the transversal and in corresponding positions (one inside and one outside the lines). They are equal if the lines are parallel.

5. Vertical Angles: These angles are opposite each other when two lines intersect. They are always equal.

6. No Relationship: If none of the above conditions are met, then the angles do not have a specific relationship.

Now, let’s categorize the given angle pairs based on the relationships defined above:

1. <13 and <2: This depends on their specific positions, but if they are alternate interior angles with respect to a transversal, they would be equal. If they do not match any of the above conditions, they can be considered "no relationship".

2. <7 and <9: If they are on the same side of the transversal and inside the two lines, they would be same side interior angles.

3. <16 and <5: Depending on their positions, if <16 is on the opposite side of the transversal to <5 and both are interior angles, they could be alternate interior angles.

4. <17 and <23: Depending on their relative positions, this could be alternate exterior angles, assuming <17 is outside the line with respect to <23, depending on how the transversal intersects.

5. <10 and <13: If one is on the same side of the transversal and corresponding to the other, they could be corresponding angles.

To provide a definitive classification, the spatial arrangement of these angles is key. If you can clarify the specific orientation or layout of these angles, I can provide more accurate classifications!