Question

The angles of ${\Delta }_{ls}$ are in AP the least angle is half of the greatest angle find the angles.

Answer 1

Let the angle are $a-r,a,a+r$ [$\because$ they are in A.P]

Sum of angles $={180}^0$

$\Rightarrow 3a={180}^0\Rightarrow a={60}^0$

Also $a-r=\frac{1}{2}(a+r)\Rightarrow 2a-2r=a+r$

$\Rightarrow a=3r$

$\Rightarrow r={20}^0$

Therefore the angles are $={60}^0-{20}^0,{60}^0,{60}^0+{20}^0$

$={40}^0,{60}^0,{80}^0$