If the difference of two acute angles of a right angled trangled is `(2pi)/(5)` then find the sexagesimal values of two angles.

Explanation

Let the two angles be `x^(@) "and" y^(@)`.
`therefore x-y=(2x)/(5) or, x-y=(2xx180)/(5)`
or, `" "x-y=72………….(1)`
Also, x+y = 90 ………………..(2)
Adding (1) and (2) we get, 2x = 162 or , `x=(162)/(2) = 81`
`therefore 81 + y =90 or, y = 90 -81 =9`
Hence the equried angles are `81^(@) and 9^(@)`.