Question

The angles of a triangle are in the ratio 2:3:4 .find the measure of each angle

Answer 1

Given-

Ratio of the Angles of the triangle=2:3:4

Measures of angles of a triangle =180°

Therefore,

Let the common multiple of ratio of the angles be x

Thereafter we get,

2x+3x+4x=180°

9x=180°

x=180°/9

x=20

Now, finding measure of each angle

1)Angle 1 = 2x

=2 × 20

=40°

2)Angle 2 = 3x

= 3 × 20

=60°

3)Angle 3 = 4x

= 4 × 20

= 80°

Hope it helps and be of some use to u!

Answer 2

$\huge\mathfrak\green{ᴀɴsᴡᴇʀ}$

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 $9x =180^{0}$

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

$∴2x=2×20={40}^{0}$

$3x=3×20= {60}^{0}$

$and \: 4x=4×20 = {80}^{0}$

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