There are three angles. The second angle is one-third of the compliment of the first angle. The third angle is half of the supplement of the first angle. The third angle is 6 times the second angle. Find the first angle.

Options

A. `45^(@)`
B. `60^(@)`
C. `75^(@)`
D. `90^(@)`

Answer

B

Explanation

Let the first angle, the second angle, and the third angle be f, s and t, respectively.
`s=((90^(@)-f)/(3))=(30^(@)-(f)/(3))`
`t=((180^(@)-f)/(2))=(90^(@)-(f)\(2))`
t=6s
`:. (90^(@)-(f)/(2))=6(30^(@)-(f)/(3))`
`implies (90^(@)-(f)/(2))=(180^(@)-2f)`
`f=60^(@)`
Hence, the correct option is (b)