Question

Question 8
The angles of a triangle are in the ratio 2 : 3 : 4. Find the angles of the triangle.

Answer 1

Angles are in the ratio 2 : 3 : 4.
Let the angles of a triangle be $\angle A,\angle Band\angle C$.
$\therefore \angle A=2x,\angle B=3x,$
$\angle C=4x$
$In\Delta ABC,\angle A+\angle B+\angle C={180}^{\circ }$
[Sum of all the angles of a triangle is ${180}^{\circ }$]
$\Rightarrow 2x+3x+4x={180}^{\circ }$
$\Rightarrow 9x={180}^{\circ }$
$\Rightarrow x=\frac{{180}^{\circ }}{9}={20}^{\circ }$
$\therefore \angle A=2x=2\times {20}^{\circ }={40}^{\circ }$
$\angle B=3x=3\times {20}^{\circ }={60}^{\circ }$
$And\angle C=4x=4\times {20}^{\circ }={80}^{\circ }$