Final answer:
The arc measure of arc (DE) in degrees is calculated based on the fraction of the circle's circumference that the arc represents, multiplied by 360. For precise measurements, specific calculations using the circle's radius and the central angle are required.
Step-by-step explanation:
The question asks about the arc measure of arc (DE) in degrees. To determine the arc measure, we use the fact that a complete revolution of a circle is equivalent to 360 degrees. If we know the fraction of the circle that arc (DE) represents, we can multiply that by 360 to obtain the arc measure in degrees. For example, if arc (DE) is half of the circle, the arc measure would be 360/2 = 180 degrees. If the specific fraction or portion of the circle that arc (DE) spans is not provided, we would need additional information such as the central angle corresponding to arc (DE) or the radius and arc length to calculate the measure of the arc.
When dealing with arc length, we can use the formula Δθ = 2πr for a complete revolution, where r is the radius of the circle. For a partial revolution or arc, we use a proportion of this formula. For example, if arc (DE) is a quarter of the circle's circumference, the arc length in terms of the angle of rotation (Δθ) would be πr/2, and if we convert this radian measure into degrees, it would correspond to a 90-degree arc.
In scenarios where precision is key, and the arc spans a considerable portion of the circle, using approximations such as the straight-line distance would not be accurate, and actual calculations based on the circle's geometry are necessary.