Question

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

Answer 1

Answer:

Let’s assume a triangle ABC with angles, <A, <B and <C.

Given, <A : <B : <C is equal to 2:3:4, let’s assume the values of angles as,

<A = 2x

<B = 3x

<C = 4x,

x is a whole number. You can see that we have taken the values of angles such that they are still in the ratio 2:3:4.

Now, we know that the sum of all the angles of a triangle is 180°.

So, in triangle ABC

<A + <B + <C = 180°

Putting values of angles,

2x + 3x + 4x = 180°

9x = 180°

x = 180°/9

x = 20°

So, angles are as follows,

<A = 2(x) = 2(20°) = 40°

<B = 3(x) = 3(20°) = 60°

<C = 4(x) = 4(20°) = 80°

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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 $9x =180^{0}$

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

$∴2x=2×20={40}^{0}$

$3x=3×20= {60}^{0}$

$and \: 4x=4×20 = {80}^{0}$

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