Angles of a triangle are in the ratio 2: 4: 3 | vedclass

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Question

(A) Given that: The ratio of the angles of a triangle is $2: 4: 3$.Let the angles of the triangle be $\angle A, \angle B$,and $\angle C$.Therefore,$\a

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(A) Given that: The ratio of the angles of a triangle is $2: 4: 3$.Let the angles of the triangle be $\angle A, \angle B$,and $\angle C$.Therefore,$\angle A = 2x, \angle B = 4x$,and $\angle C = 3x$.In $	riangle ABC$,the sum of the angles is $\angle A + \angle B + \angle C = 180^{\circ}$.[Since the sum of the interior angles of a triangle is $180^{\circ}$].Substituting the values: $2x + 4x + 3x = 180^{\circ} \Rightarrow 9x = 180^{\circ} \Rightarrow x = 180^{\circ} / 9 = 20^{\circ}$.Calculating the angles:$\angle A = 2x = 2 	imes 20^{\circ} = 40^{\circ}$.$\angle B = 4x = 4 	imes 20^{\circ} = 80^{\circ}$.$\angle C = 3x = 3 	imes 20^{\circ} = 60^{\circ}$.Comparing the angles $40^{\circ}, 80^{\circ}$,and $60^{\circ}$,the smallest angle is $40^{\circ}$.

Angles of a triangle are in the ratio $2: 4: 3$. The smallest angle of the triangle is (in $^{\circ}$)

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