Question

if the angles of a triangle are in ratio 2:3:4 then find the measure of each angle​

Answer 1

$\huge\mathfrak\green{ᴀɴsᴡᴇʀ}$

ᴀɴɢʟᴇ sᴜᴍ ᴘʀᴏᴘᴇʀᴛʏ ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇ ɪs 180 ᴅᴇɢʀᴇᴇs. ɪᴛ ɪs ɢɪᴠᴇɴ ᴛʜᴀᴛ ᴛʜᴇ ᴀɴɢʟᴇs ᴀʀᴇ ɪɴ ᴛʜᴇ ʀᴀᴛɪᴏ $2:3:4$

sᴏ ʟᴇᴛ ᴜs ᴄᴏɴsɪᴅᴇʀ ᴛʜᴇ ᴀɴɢʟᴇs ᴀs $2x,3x$ ᴀɴᴅ $4x.$

$2x+3x+4x=9x$

$Angle \: sum \: of \: triangle = 180$

sᴏ $9x =180^{0}$

$or \: x= \frac{9}{180} ={20}^{0}$

$∴2x=2×20={40}^{0}$

$3x=3×20= {60}^{0}$

$and \: 4x=4×20 = {80}^{0}$

$∴ the \: angles \: are  {40}^{0}, {60}^{0},{80}^{0}$