Find the degree measure of the angles subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm `(U s e\ pi=22//7)` .

Explanation

We know that in a circle of radius `r` unit, if an arc of length 1 unit subtends an angle `theta` radian at the centre, then `theta=frac{1}{r}`


Therefore, for `{r}=100 {~cm}, 1=22 {~cm}`, we have



`theta=frac{22}{100} text { radian }=frac{180}{pi} times frac{22}{100} text { degree }=frac{180 times 7 times 22}{22 times 100} text { degree } `


`=frac{126}{10} text { degree }=12 frac{3}{5} text { degree }=12^{circ} 36^{prime},[because 1^{circ}=60^{prime}]`