Solution

We know that in a circle of radius $$r$$ unit, if an arc of length $$l$$ unit subtends an angle $$\theta$$ radian at the centre, then $$\displaystyle\theta=\frac{l}{r}$$.
It is given that $$r = 75$$ cm

(i) $$ l = 10$$ cm

$$\therefore \displaystyle\theta=\frac{10}{75}=\frac{2}{15}$$ radian

(ii) $$ l = 15$$ cm

$$\therefore \displaystyle\theta=\frac{15}{75}=\frac{1}{5}$$ radian

(iii) $$ l = 21$$ cm

$$\therefore \displaystyle\theta=\frac{21}{75}=\frac{7}{25}$$ radian