Question

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

Answer 1

Let theree angles of a triagle be

$x^{\circ },(x+10{)}^{\circ },(x+20{)}^{\circ }$

But sum of three angles of a triangles of a triangles is ${180}^{\circ }$

$\therefore x+(x+10{)}^{\circ }+(x+20)={180}^{\circ }$
$\Rightarrow x+x+{10}^{\circ }+x+20={180}^{\circ }$
$\Rightarrow 3x+{30}^{\circ }={180}^{\circ }$
$\Rightarrow 3x={180}^{\circ }-{30}^{\circ }={150}^{\circ }$
$\therefore x=\frac{150}{3}={50}^{\circ }$
$\therefore$ Angle are ${50}^{\circ }$,50+10,50+20
i.e.${50}^{\circ },{60}^{\circ },{70}^{\circ }$