Question

If angles of the triangle are in the ratio 2:3:4. find the value of each angle? ​

Answer 1

Answer :-

• The angles are 40°, 60° and 80° respectively.

Given :-

• The angles of the triangle are in the ratio 2 : 3 : 4.

To find :-

• The value of each angle.

Step-by-step explanation :-

The angles of the triangle are in the ratio 2 : 3 : 4.

So, let the angles be 2x, 3x and 4x respectively.

We know that the sum of all the angles in a triangle = 180°.

Thus, we have :-

$\sf2x + 3x + 4x = 180^{\circ}$

$\sf5x + 4x = 180^{\circ}$

$\sf9x = 180^{\circ}$

$\sf \: x = \dfrac{180^{\circ}}{9}$

$\sf \: x = 20^{\circ}.$

Since the value of x = 20°, therefore the value of the angles are as follows :-

$\sf2x = 2 \times 20^{\circ} = 40^{\circ}.$

$\sf3x = 3 \times 20^{\circ} = 60^{\circ}.$

$\sf4x = 4 \times 20^{\circ} = 80^{\circ}.$

Thus, the angles are 40°, 60° and 80°.

Verification :-

To verify your answer, just add them up and see if their value is 180°. (The sum of all the angles of a triangle)

20° + 60° + 80° = 180°.

Since the angles make up 180°,

Hence verified ✔️✔️

Answer 2

$\Huge \fbox{Aɴsᴡᴇʀ}$

$\large \underline { \underline{ \frak{ \color{red}ɢɪᴠᴇɴ::}}}$

${\mapsto \sf{ Angle \: of \: triangle_{(in \: ratio)}=2:3:4}}$

$\large \underline { \underline{ \frak{ \color{re}Tᴏ \: ғɪɴᴅ::}}}$

$\leadsto \sf{Angle \: of \: triangle. }$

$\large \underline { \underline{ \frak{ \color{indigo}Cᴏɴᴄᴇᴘᴛ \: ᴜsᴇᴅ::}}}$

${ \mapsto \sf{Sum \: of \: angle \: of \: triangle \: is \: 180 \degree.} }$

$\large \underline { \underline{ \frak{ \color{blue}Aᴄᴄᴏʀᴅɪɴɢ \: ᴛᴏ \: ϙᴜᴇsᴛɪᴏɴ::}}}$

$\dashrightarrow \sf{2x°+3x°+4x°=180°}$

$\dashrightarrow \sf{9x=180°}$

$\dashrightarrow \sf{x=20°}$

$\bf \underline{Hᴇɴᴄᴇ,}$

$\implies \sf{2x°=2×20=40°}$

$\implies \sf{3x°=3×20=60°}$

$\implies \sf{4x°=4×20=80°}$

$\large \underline { \frak{ \pink{Vᴇʀɪғɪᴄᴀᴛɪᴏɴ : : }}}$

$\longrightarrow \sf{2x°+3x°+4x°=180°}$

$\longrightarrow \sf{40° + 60° + 80°=180°}$

$\longrightarrow \sf{180°=180°}$

$\longrightarrow \sf{L.H.S.=R.H.S.}$