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

Q. the angles of triangle are in A.P. The greatest angle is twice the

1.	Q. the angles of triangle are in A.P. The greatest angle is twice the least. Find all the angles
Answer» Let the three angles of triangle which are in A.P. be a - d, a, a + dNow, sum of the angles = 180°{tex}\\Rightarrow{/tex}\xa0a - d + a+ a + d =\xa0180°{tex}\\Rightarrow{/tex}\xa03a = 180°{tex}\\Rightarrow{/tex}\xa0a = 60°It is given that,a + d= 2(a - d){tex}\\Rightarrow{/tex}\xa0a + d = 2a - 2d{tex}\\Rightarrow{/tex}\xa0a = 3d{tex}\\Rightarrow{/tex}\xa060° = 3d{tex}\\Rightarrow{/tex}\xa0d =\xa020°Thus, the angles of triangle are 40°, 60°, 80°.