Question

The angles of a triangle are in AP and the greatest angle is double the least. Find all the angles.

Answer 1

Since angles are in A.P let angles be

$\alpha ,\alpha +d,\alpha +2d$

Then,

$\alpha +\alpha +d+\alpha +2d=180\Rightarrow 3\alpha +3d=180$

Since $2\alpha =\alpha +2d$

$\Rightarrow \alpha =2d$

$\Rightarrow 3(\alpha +d)=180$

$\Rightarrow \alpha +d=60$

$\Rightarrow 2d+d=60$ $(\alpha =2d)$

$\Rightarrow d=20$

$\Rightarrow \alpha =40$

$\Rightarrow$ angles are $40,60,80$.