The core concept is that the length of the wire remains constant. The circumference of the smaller circle becomes the arc length on the larger hoop.

1. Calculate the length of the wire:
The length of the wire is the circumference of the circle it forms initially.
Radius of the initial circular wire, \(r_1 = 7.5\) cm.
Circumference, \(L = 2\pi r_1 = 2\pi(7.5) = 15\pi\) cm.

2. Use the arc length formula to find the subtended angle:
This length \(L\) now forms an arc on a larger hoop.
Radius of the hoop, \(r_2 = 120\) cm.
The formula for arc length is \(L = r_2 \cdot \theta\), where \(\theta\) is the angle in radians.
We can substitute our known values to solve for \(\theta\):
\[\begin{aligned} 15\pi &= 120 \cdot \theta_{\text{rad}} \\ \theta_{\text{rad}} &= \frac{15\pi}{120} \\ \theta_{\text{rad}} &= \frac{\pi}{8} \text{ radians} \end{aligned}\]
3. Convert the angle from radians to degrees:
To convert an angle from radians to degrees, we multiply by the conversion factor \(\frac{180^\circ}{\pi}\).
\[\theta_{\text{deg}} = \frac{\pi}{8} \times \frac{180^\circ}{\pi} = \frac{180^\circ}{8} = 22.5^\circ\]
4. Convert decimal degrees to degrees and minutes:
The answer options are in degrees and arcminutes (′). The value \(22.5^\circ\) consists of 22 full degrees and 0.5 of a degree.
To convert the decimal part to minutes, we multiply by 60, since \(1^\circ = 60'\).
\[0.5 \times 60' = 30'\]
Therefore, \(22.5^\circ\) is equal to \(22^\circ30'\).

Result:
The angle subtended at the centre of the hoop is \(22^\circ30'\).