1.Explain the relationship(s) among angle measure in degrees, angle measure in radians, and arc length.

we all know that a circle has 360°

we all know that the circumference of a circle is 2πr

a radian is the angle which subtends an arc length equal to the radius.

So, since C=2πr, a circle has 2π radians.

So, 2π radians = 360°

Thank you so much steve

The relationship among angle measure in degrees, angle measure in radians, and arc length can be explained using a formula derived from the definition of a circle.

1. Angle Measure in Degrees: Degree is a unit of measurement used to quantify the size of an angle. A circle is divided into 360 degrees. So, each degree represents 1/360th of a full circle.

2. Angle Measure in Radians: Radian is another unit of measurement used for angles, particularly in trigonometry and calculus. A radian is defined as the angle subtended at the center of a circle by an arc that has the same length as the radius of the circle. In other words, a full circle has an angle measure of 2π radians, where π (pi) is a mathematical constant approximately equal to 3.14159.

3. Arc Length: Arc length is the distance along the circumference of a circle. It is related to the angle measure by a formula derived from the definition of a circle. The formula is:

Arc Length = (Angle Measure / 360) * 2πr

In this formula, "r" represents the radius of the circle.

So, the relationship among angle measure in degrees, angle measure in radians, and arc length is given by the formula above. By knowing the angle measure in degrees or radians, and the radius of the circle, you can calculate the arc length. Conversely, if you know the arc length and the radius, you can calculate the angle measure in degrees or radians.