Circumference and Area

Let the radius of the smaller circle be r, the angle of the sector be θ.

The perimeter of the sector
= 3r + 3r + 3r × 2π × θ/360°
= r × (6 + θπ/60°)

The perimeter of the smaller circle
= 2πr

⇒ r × (6 + θπ/60°) = 2πr
6 + θπ/60° = 2π
θ = 60° × (2π - 6)/π
θ = 5.41°

∴ The angle of the sector is 5.41°.