Question

A circle has radius 16 units and a central angle with arc length 4pi.

A second circle has radius 5 units and a central angle with arc length 5pi.
How do the measures of the 2 angles compare? Explain or show your reasoning.
The first circle's angle has an arc length to radius ratio of [Select]
ratio of [Select]
Since the ratio is [Select)
[Select]
The second has an arc length to radius
in the second circle, the central angle in that circle is

Answer 1

Circle with radius 16 and arc length 4pi= Central angle: 45 degrees

Circle with radius 5 and arc length 5pi= Central angle: 180 degrees

Explanation:

Answer:

Circle with radius 16 and 4pi arc length: central angle: 45 degrees

Explanation:

I am not too sure about what are the options to select, but I found the angle measures of the 2 circles! For finding the angle measure, I used the formula: Central angle/360=arc length/2•pi•r. The first circle has a radius of 16, and a arc length of 4•pi. X can be used to represent the central angle since it remains unknown. When we plug in those values, we get x/360=4•pi/2•pi•16. Using inverse operations o that we can isolate for x, we can multiply 360 by both sides. x=(4•pi/2•pi•16)•360. I just use parentheses to not mix up the numbers shown. Then, I use desmos scientific calculator for calculating the central angle, which is 45 degrees. There appears to be a second circle as well. With a radius of 5, and arc length of 5pi. The equation to represent this is, x/360=5•pi/2•pi•5. Using the same steps as before, which is multiplying 360 for each side, we get x=(5•pi/2•pi•5)360. Using the desmos scientific calculator, we get the central angle is equal to 180 degrees. I am unsure about the other parts for selecting options. Sorry, this is what I got, and best of wishes for you! I hope it helps