Final answer:
The student's question involves identifying and defining certain types of angles in geometry. Without a visual figure, it's not possible to categorically determine which angles are being described. The answer provides general knowledge on complementary, supplementary, and vertical angles, as well as how they pertain to arc length and angle measurements.
Step-by-step explanation:
The student's question involves identifying types of angles based on their positions. In the context provided, it appears the student is dealing with geometric figures and properties of angles. To answer the question correctly, one would fill in the blanks with specific types of angles, such as 'complementary' or 'alternate interior' angles, depending on the figure in the question, which seems to have been omitted. Since the question refers to angles 1 and 5, and angles 4 and 6, without a visual figure, it is not possible to definitely categorize these angles. However, we can discuss general principles concerning the relationships of angles:
- Complementary angles are two angles whose sum is 90 degrees.
- Supplementary angles are two angles whose sum is 180 degrees.
- Vertical angles are opposite angles formed by the intersection of two lines and are always equal.
- Alternate interior angles are formed when a transversal passes through two lines, and these angles are equal if the lines are parallel.
Arc length and rotation principles relate to angles as well, as seen in the provided references to Figure 6.4, explaining that points equidistant from the center of rotation that rotate through the same angle will have different arc lengths if they are at different radii from the center. This is important in understanding circular motion and the geometry of circles.
A discussion about how angles are measured includes units of degrees, minutes of arc, and seconds of arc. This measurement system is crucial for precise geometric calculations and is distinct from the units of time, despite the similar terminology.