Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm.

Radius of the circle, r = 100 cm

Length of the arc, l = cm

Angle in radians: $$\theta = \frac{l}{r}​$$​​

Conversion from radians to degrees: $$\theta_{\text{degrees}} = \theta \times \frac{180}{\pi}$$​​

Calculate the angle in radians:

​$$\theta = \frac{22}{100} = 0.22 \text{ radians}$$​​

Convert θ to degrees:

​$$\theta_{\text{degrees}} = 0.22 \times \frac{180}{\pi} ​$$​​

Using $$\pi = \frac{22}{7}$$​:

​$$\theta_{\text{degrees}} = 0.22 \times \frac{180\times 7}{22}$$​​

= $$12^\circ 36’$$​​

Thus, The degree measure of the angle is $$12^\circ 36’$$​ .