Answer:
[tex]\boxed{\boxed{\theta=150^{\circ}}}[/tex]
Step-by-step explanation:
We know that,
[tex]\text{Arc length}=r\cdot \theta[/tex]
where,
r = radius,
θ = central angle in radian.
Given,
diameter = 6 m, so radius = 3 m.
[tex]\text{Arc length}=\dfrac{5}{2}\pi[/tex]
Putting the values,
[tex]\Rightarrow \dfrac{5}{2}\pi=3\theta[/tex]
[tex]\Rightarrow \theta=\dfrac{5}{2\times 3}\pi[/tex]
[tex]\Rightarrow \theta=\dfrac{5}{6}\pi=\dfrac{5}{6}\times 180^{\circ}=150^{\circ}[/tex]
