Question

The angles of a triangle are in AP. The greatest angle is twice the least. Find the difference between largest angle and smallest angle

Answer 1

Let the angles be $a-d,a,a+d$, where $a$ and $d$ are first term and common difference respectively.
$\therefore a-d+a+a+d=180$ ($\because \text{sum of angles of trianlge}$)
$3a=180\Rightarrow a=60$
Also, $a+d=2(a-d)$ (Given)
$\Rightarrow 60+d=2(60-d)$
$\Rightarrow 3d=60\Rightarrow d=20$
Therefore, angles are $60-20,60,60+20i.e.40,60,80$

Difference $=80-40=40$