The angles of a triangle are successively in equal difference. If the number of degrees in the greatest angle be same as the number of grades in the least one . Find the angles in degrees.

Explanation

Let the angle are (a-d), a,(a+d) degees respectively.
`therefore a-d+a+a+d=180^(@)[therefore "the sum of angles of a triangles is" 180^(@)]`
or, " "`3a=180^(@)" "or," "a=(180^(@))/(3)=60^(@)`
Here, the least angle is (a-d) degree
`=(10)/(9)(a-d) "grades "[therefore 90^(@)=100^(g)]` and the greatest angle is (a-d) degrees.
As per question, `a+d =(10)/(9)(a-d)`
or,`" "` 9a+9d=10a-10d
or,`" " `9d+10d=10a-9a
or, `" "` 19d=a
or,`" "`19d=60[`thereforea=60`]
or," "`d=(60)/(19)`
Hence the angles are `(60-(60)/(19)) "degrees, 60 degrees and" (60+(60)/(19))` degrees,
or,`56(16)/(19)"degrees,60 degrees and " 63+(3)/(19)` degrees.