a circle has a circumference of 6. it has an arc of length 1.\n\nwhat is the central angle of the arc, in…

Explanation:

Step1: Identify the ratio of arc length to circumference

The ratio of the arc length $s$ to the total circumference $C$ is equal to the ratio of the central angle $\theta$ to the total degrees in a circle ($360^{\circ}$). $$ \frac{\text{Arc Length}}{\text{Circumference}} = \frac{\text{Central Angle}}{360^{\circ}} $$

Step2: Substitute the given values into the ratio

Given arc length $s = 1$ and circumference $C = 6$. $$ \frac{1}{6} = \frac{\theta}{360^{\circ}} $$

Step3: Solve for the central angle

Multiply both sides by $360^{\circ}$ to isolate $\theta$. $$ \theta = \frac{1}{6} \times 360^{\circ} $$

Step4: Calculate the final value

Perform the division. $$ \theta = 60^{\circ} $$

Answer:

60^{\circ}