Question

if the angles of a triangle are in the ratio 7:5:3 , the triangle will be​

Answer 1

$Let \: \angle A , \angle B \:and \: \angle C \: are \\ 3 \: angles \:of \: a \: \triangle ABC .$

$\angle A : \angle B : \angle C = 7 : 5 : 3 \: (given)$

$Let \: \angle A = 7x ,\\\angle B = 5x ,\:and \\\angle C = 3x$

$\boxed { \pink {\angle A + \angle B + \angle C = 180\degree}}$

$\blue { ( Angle \: Sum \: property )}$

$\implies 7x + 5x + 3x = 180$

$\implies 15x = 180$

$\implies x = \frac{180}{15}$

$\implies x = 12$

$\angle A = 7x = 7\times 12 = 84 \degree$

$\angle B = 5x = 5\times 12 = 60 \degree$

$\angle C = 3x = 3\times 12 = 36 \degree$

$All\: 3 \:angles \:are \: 84\degree, 60\degree \:and \:36\degree \\less \:than \: 90\degree .$

$\triangle ABC \: is \:a \: \green { Acute \:angle \: triangle }.$

$Therefore.,$

$\red { The \: triangle \:will \: be }$

$\green { \:Acute \:angle \: triangle }.$

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