Final answer:
The reference angle for a -287° angle is 73°, which is the acute angle made with the x-axis, calculated by adding 360° to the original negative angle until it is positive.
Step-by-step explanation:
The measure of the reference angle for a -287° angle is the acute angle that the terminal side of the angle makes with the x-axis. Since angles are usually measured in the counter-clockwise direction from the positive x-axis, we first need to determine the equivalent positive angle for -287° by adding 360° until we get a positive angle. Adding 360° to -287° gives us 73°, which means the angle is in the first quadrant, and thus its reference angle is 73°.
When computing angles, trigonometric relationships often come into play, especially when using functions like sine, cosine, or tangent and their inverses for angles in different quadrants. It's also important to remember that an angle's reference angle is always between 0° and 90°, regardless of its original measure.