Question

The three angles are in ratio $2:3:5$. find the measure of each angle. classify the triangle

Answer 1

Given: Ratios $=2:3:5$

Let common factor of the ratio of angles is $x.$

the three angles will be $2x,3x,5x.$

So, $2x+3x+5x={180}^{\circ }$ [sum of three angles of a triangle is ${180}^{\circ }$]
$\Rightarrow 10x={180}^{\circ }$
So, $x={18}^{\circ }$

$\therefore$ three angles are

$2x=2\times {18}^{\circ }={36}^{\circ }$

$3x=3\times {18}^{\circ }={54}^{\circ }$

$5x=5\times {18}^{\circ }={90}^{\circ }$

Hence angles are ${36}^{\circ },{54}^{\circ },$ and ${90}^{\circ }.$

It is a right-angled triangle.