Question

the angle of a triangle are in the ratio 2:4:3. the smallest angle of the triangle is?​

Answer 1

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Answer 2

Given that :-

$\sf \pink {The\: ratio\: of\: angles \:of\: a \:triangle\: is\: 2:4:3.}$

$\sf \green {Let}$

$\sf \purple{The \:angles \:of\: the\: triangle\: be \:∠ A , ∠ B \:and \:∠ C}$

$\sf \orange \therefore \red{ ∠ A = 2x,∠ B = 4x \:and \:∠ C = 3x}$

$\sf \blue {In \:∠ ABC , ∠ A + ∠ B + ∠ C = 180°}$

$\sf \blue \therefore \green{Sum \:of\: angles \:of\: a \:triangle\: is \:180°}$

$\sf \purple \therefore \pink{ 2x+4x+3x=180°}$

$\sf \green \implies \blue {9x=180°}$

$\sf \red \implies \orange {x=\cancel\frac{180}{9}}$

$\sf \pink \implies \purple{20°}$

$\sf \blue \therefore\green{∠ A = 2x}\\ \sf =2×20°\\ \sf =40°$

$\sf \orange \implies \red {∠ B = 4x}\\ \sf =4×20°\\ \sf=80°$

$\sf \purple \implies \pink {∠ C = 3x}\\ \sf =3×20°\\ \sf=60°$

$\sf \blue {Hence,}$

$\sf \green {The \:smallest \:angles\: of\: a \:triangle \:is \:40°}$