Answer:
108°
Step-by-step explanation:
[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right) \quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}[/tex]
Given:
- diameter = 10 km ⇒ radius (r) = 5 km
- Arc length = 3π km
Substituting the given values into the formula and solving for [tex]\theta[/tex]:
[tex]\implies 3 \pi=2 \pi (5)\left(\dfrac{\theta}{360^{\circ}}\right)[/tex]
[tex]\implies 3 =10\left(\dfrac{\theta}{360^{\circ}}\right)[/tex]
[tex]\implies 3 \cdot 360^{\circ} =10\:\theta[/tex]
[tex]\implies \theta=\dfrac{1080^{\circ}}{10}[/tex]
[tex]\implies \theta={108^{\circ}[/tex]
