Question

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

Answer 1

Suppose the angles of a triangle are (a − d), a , (a + d) such that , (a + d) >a > (a − d).

$$\begin{gathered} a-d+a+a+d=180\left[\mathrm{angle}\mathrm{sum}\mathrm{property}\right] \\ \Rightarrow 3a=180 \\ \Rightarrow a=60 \\ \mathrm{Now},\left(a+d\right)=2\left(a-d\right) \\ \Rightarrow a+d=2a-2d \\ \Rightarrow a=3d \\ \Rightarrow d=\frac{60}{3}=20 \\ \mathrm{Therefore},\mathrm{the}\mathrm{three}anglesofatriangle\mathrm{are}40,60,80. \end{gathered}$$