a circle has a circumference of 20. it has an arc of length 4.\nwhat is the central angle of the arc, in…

Explanation:

Step1: Identify the arc length formula

The arc length $s$ is a fraction of the total circumference $C$, proportional to the central angle $\theta$ in degrees. $$s = \frac{\theta}{360^{\circ}} \times C$$

Step2: Substitute the given values

Given circumference $C = 20$ and arc length $s = 4$. $$4 = \frac{\theta}{360^{\circ}} \times 20$$

Step3: Solve for the central angle

Divide both sides by 20 and then multiply by $360^{\circ}$. $$\frac{4}{20} = \frac{\theta}{360^{\circ}}$$ $$\frac{1}{5} = \frac{\theta}{360^{\circ}}$$ $$\theta = \frac{360^{\circ}}{5}$$

Step4: Calculate the final value

Perform the division to find the angle in degrees. $$\theta = 72^{\circ}$$

Answer:

72^{\circ}