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

Explanation:

Step1: Identify the relationship between arc length and 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 ($360^{\circ}$). $$ \frac{s}{C} = \frac{\theta}{360^{\circ}} $$

Step2: Substitute the given values into the formula

Substitute the arc length $s = 4$ and the circumference $C = 20$ into the equation. $$ \frac{4}{20} = \frac{\theta}{360^{\circ}} $$

Step3: Simplify the fraction

Reduce the fraction on the left side of the equation. $$ \frac{1}{5} = \frac{\theta}{360^{\circ}} $$

Step4: Solve for the central angle

Multiply both sides by $360^{\circ}$ to find the value of $\theta$. $$ \theta = \frac{1}{5} \times 360^{\circ} $$ $$ \theta = 72^{\circ} $$

Answer:

72^{\circ}