Final answer:
The arc length for an angle measure of 180° is half the circumference of the circle, which is πr where r is the radius of the circle.
Step-by-step explanation:
If the angle measure for an arc is 180°, then the arc length is half the distance around the circle. Since the angle of rotation is the arc length divided by the radius, and a complete rotation of 360° yields an arc length equal to the circumference (which is 2πr for a circle with radius r), an arc of 180° specifically represents half of a full rotation. Therefore, the arc length for an angle of 180° will be πr, which is half the circumference of the circle. This relationship can also be seen as the proportion – the arc degree measure (180°) over the total degrees in a circle (360°) equals the arc length over the circumference. Hence the formula –180° / 360° = arc length / (2πr)– simplifies to arc length = πr.