Question

Question 8
Angles of a triangle are in the ratio 2 : 4 : 3. The smallest angle of the triangle is:

A) ${60}^{\circ }$
B) ${40}^{\circ }$
C) ${80}^{\circ }$
D) ${20}^{\circ }$

Answer 1

Angles are in the ratio 2 : 4 : 3.
Let the angles of a triangle be
$\angle A,\angle Band\angle C$.
$Let\angle A=2x,\angle B=4x,\angle C=3x$

$In\Delta ABC,\angle A+\angle B+\angle C={180}^{\circ }$
[Sum of all the angles of a triangle is ${180}^{\circ }$]
$\Rightarrow 2x+4x+3x={180}^{\circ }$
$\Rightarrow 9x={180}^{\circ }$
$\Rightarrow x=\frac{{180}^{\circ }}{9}={20}^{\circ }$

$\therefore \angle A=2x=2\times {20}^{\circ }={40}^{\circ }$
$\angle B=4x=4\times {20}^{\circ }={80}^{\circ }$
$and\angle C=3x=3\times {20}^{\circ }={60}^{\circ }$

Hence, the smallest angle of triangle is ${40}^{\circ }$.