Let `theta` be a positive angle. If the number of degrees in `theta` is divided by the number of radians in `theta`, then an irrational number `180/pi` results. If the number of degrees in `theta` is multiplied by the number of radians in `theta`, then an irrational number `(125pi)/9` results. The angle `theta` must be equal to

Options

A. `30^(@)`
B. `45^(@)`
C. `50^(@)`
D. `60^(@)`

Answer

C

Explanation

From going by the options ,
option (a) , `theta=30^(@)` , as we know that
`180^(@)=pi` radian
Now according to question,
`(30^(@)xx180^(@))/(30^(@)pi)=(180)/(pi)`
Now number of degree in `theta` is multipled by number of radians in `theta`.
`therefore30^(@)xx(30pi)/(180)=(900pi)/(180)=(10pi)/(2)=5pine(125pi)/(9)`
From option (b) ,
`theta=45^(@)`
`therefore45^(@)=(45^(@)pi)/(180)` radian
Now according to question ,
`(45^(@)xx180)/(45^(@)pi)=(180)/(pi)`
Now number of degree in `theta` is multiplied by number of radian in `theta`.
`therefore45^(@)xx(45^(@)pi)/(180^(@))=(45pi)/(4)ne(125pi)/(9)`
From option (c ) ,
`theta=50^(@)`
As we know that `180^(@)=pi` radian
Now according to question
`(50^(@)xx180^(@))/(50^(@)pi)=(180)/(pi)`
Now number of degree in `theta` is multiplied by number of radian in `theta` .
`therefore50^(@)xx(50pi)/(180)=(2500pi)/(180)=(125pi)/(9)`
`therefore` Option (c) is correct.