Final answer:
The complement and supplement of an angle relate to the amount by which an angle must be increased to 90 degrees (complement) or 180 degrees (supplement). Mathematical quantities does the complement and supplement of each angle calculator find is C) Angles and their complements.
Step-by-step explanation:
The complement and supplement of an angle refer to specific mathematical quantities related to angles in geometry. The complement of an angle is the amount needed to add to the angle to make a right angle (90 degrees). Conversely, the supplement of an angle is the amount needed to add to the angle to make a straight angle (180 degrees).
The use of trigonometry is essential in understanding these concepts, especially when dealing with right triangles, as explained by trigonometric ratios such as sine, cosine, and tangent.
For example, using trigonometric identities such as sin(2θ) = 2sin(θ)cos(θ) and cos(2θ) = cos2(θ) - sin2(θ), one can derive further relationships between angles and their respective complements or supplements.
Therefore, the correct answer to which mathematical quantities the complement and supplement of each angle calculator find is C) Angles and their complements.