Question

ᴛʜᴇ ᴛʜʀᴇᴇ ᴀɴɢʟᴇs ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇs ᴀʀᴇ ɪɴ ᴛʜᴇ ʀᴀᴛɪᴏ 1:2:3 . ғɪɴᴅ ᴛʜᴇ ᴀʟʟ ᴛʜᴇ ᴀɴɢʟᴇs ᴏғ ᴛʜᴇ ᴛʀɪᴀɴɢʟᴇs .​

Answer 1

Answer:

ʟᴇᴛ , ᴍᴇᴀsᴜʀᴇs ᴏғ ᴛʜᴇ ᴀɴɢʟᴇs ᴏғ ᴛʀɪᴀɴɢʟᴇs ʙᴇ xᵒ , 2xᵒ , 3xᵒ .

ᴛʜᴇɴ , ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴀɴɢʟᴇ sᴜᴍ ᴘʀᴏᴘᴇʀᴛʏ ᴏғ ᴛʀɪᴀɴɢʟᴇ ,

xᵒ,2xᵒ,3xᵒ = 180ᵒ

⇛ 6xᵒ = 180ᵒ

⇛ xᵒ = [ 180/6 ]ᵒ

⇛ x⁰ = 30ᵒ [ ᴀɴs ]

Answer 2

Question:-

ᴛʜᴇ ᴛʜʀᴇᴇ ᴀɴɢʟᴇs ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇs ᴀʀᴇ ɪɴ ᴛʜᴇ ʀᴀᴛɪᴏ 1:2:3 . ғɪɴᴅ ᴛʜᴇ ᴀʟʟ ᴛʜᴇ ᴀɴɢʟᴇs ᴏғ ᴛʜᴇ ᴛʀɪᴀɴɢʟᴇs .

Answer:-

• The angles of triangle are 30°,60° and 90°

Solution:-

• Ratio of angles = 1:2:3

Put x in the ratio:-

• 1x
• 2x
• 3x

• Sum of all angles = 180°

$\large{ : \implies \: x + 2x + 3x = 180}$

$\large{ : \implies \: 6x = 180}$

$\large{ : \implies \: x = \frac{180}{6} }$

$\large{ : \implies \: x = 30}$

• The value of x is 30°

Hence,

• First angle = 30°
• Second angle = 2x = 2×30 = 60°
• Third angle = 3x = 3×30 = 90°

The angles of triangle are 30°,60° and 90°