Final answer:
The angle measure of an arc that is π meters long in a circle with a 4-meter radius is 45 degrees.
Step-by-step explanation:
The question asks us to find the angle measure of an arc that is π meters long in a circle with a radius of 4 meters. The relationship between arc length (Δs), radius (r), and the angle in radians (Δθ) is given by the formula Δθ = Δs / r. Since the arc length is π meters and the radius is 4 meters, substituting these values into the formula, we have Δθ = π / 4. This simplifies to Δθ = 0.25π radians. To convert radians to degrees, we use the relationship that π radians equals 180 degrees. So, 0.25π radians is equivalent to (0.25π * 180/π) degrees, which equals 45 degrees. Therefore, the correct answer to the question is A) 45 degrees.