The angles of a triangle are in A.P. The greatest angle is twice the least. Find all the angles

Explanation

Given that, the angles of a triangle are in AP.
Let A, B and C are angles of a `triangle ABC.`
` :. B=(A+C)/(2)`
`implies 2B= A+C " " `… (i)
We know that, sum of all interior angles of a `triangle ABC=180^(@)`
`A+B+C=180^(@)`
`implies 2B+B=180^(@) " " ` [from Eq. (i)]
`implies " " 3B=180^(@)impliesB=60^(@)`
Let the greatest and least angles are A and C respectively.
`A=2C " " ` [by condition] ... (ii)
Now, put the values of B and A inEq. (i), we get
`2xx60=2C+C`
`implies120=3CimpliesC=40^(@)`
Put the value of C in Eq. (ii), we get
`A=2xx40^(@)implies A=80^(@)`
Hence, the required angles of triangle are `80^(@), 60^(@)` and `40^(@)`.