Question

The angles of a triangle are arranged in ascending order of magnitude. If the difference between two consecutive angles is ${10}^{\circ }$, find the three angles.

Answer 1

Let the three angles of a triangle be $x^{\circ },(x+10{)}^{\circ }$ and $(x+20{)}^{\circ }$

By angle sum property of triangle, sum of angles is ${180}^{\circ }$

$\therefore x^{\circ }+(x+10{)}^{\circ }+(x+20{)}^{\circ }={180}^{\circ }$

$\Rightarrow 3x^{\circ }+{30}^{\circ }={180}^{\circ }$

$\Rightarrow 3x^{\circ }={150}^{\circ }$

$\Rightarrow x^{\circ }=\frac{{150}^{\circ }}{3}$

$\Rightarrow x^{\circ }={50}^{\circ }$

Hence required angles are ${50}^{\circ },(50+10{)}^{\circ }={60}^{\circ }$ and $({50}^{\circ }+20{)}^{\circ }={70}^{\circ }$

Hence, the required angles are ${50}^{\circ },{60}^{\circ }$ and ${70}^{\circ }$