A wire of length

θ will be in degrees.

Arc-length can be given by the formula : θ / 360° × 2πr

Hence it is given that 121 cm is the arclength.

⇒ 121 = θ / 360° × 2πr

= 121 = θ / 360° × 2 × 22 / 7 × 180

= 121 = θ / 360° × 360 × 22 / 7

= 121 = θ × 22 / 7

⇒ θ = 121 × 7 / 22

= 38.5°

Hence the angle subtended at the middle is 38.5°

Which can also be written as 38° 30.’