Question

If the angles of a triangle are in the ratio of 2:3:4, then the difference of the measure of greatest angle and smallest angle is

Answer 1

Answer:

$\red {Difference \: of \: the \: measure \: of \\greatest \:angle \:and \:smallest \:angle}=\green {40\degree}$

Step-by-step explanation:

$Given \: ratio \: of \: angles \: of \: a \\triangle = 2:3:4$

$Let \: first \: angle = 2x \\second \:angle = 3x\\three \:angle = 4x$

$2x+3x+4x = 180\degree$

$\boxed { \pink {( angle \: sum \: property)}}$

$\implies 9x = 180$

$\implies x = \frac{180}{9}\\= 20$

$Difference \: of \: the \: measure \: of \\greatest \:angle \:and \: smallest \:angle\\ = 4x-2x\\=2x \\=2\times 20 \\= \green {40\degree}$

Therefore.,

$\red {Difference \: of \: the \: measure \: of \\greatest \:angle \:and \: smallest \:angle}=\green {40\degree}$

••••♪