Question

if an triangle are in the ratio 2:3:4 find the value of each angle​

Answer 1

Answer:

Let the angles are 2x, 3x and 4x. According to the angle sum property, the sum of interior angles of a triangle is 180 degree. The value of x is 20. Therefore the angles of triangle are 40, 60 and 80.

Step-by-step explanation:

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Answer 2

$\sf \orange { \underline { \sf Given :- }}$

• The ratio of three angles are in the ratio i.e., 2:3:4

$\sf \green { \underline { \sf To \: find :- }}$

• The value of each angle.

$\sf \purple { \underline { \sf Solution :- }}$

• As we know the sum of all angles of a triangle is 180°(angle sum property).
• So, let's assume that the angles are 2x, 3x, and 4x.

Thereafter,

We can write it as :-

$\bf \implies \: 2x + 3x + 4x = 180 \degree \\ \bf \implies \: 9x = 180 \\ \bf \implies \: x = \frac{ \cancel{180}}{ \cancel{9}} \\ { \underline{ \fcolorbox{black}{pink}{\bf{ \: x = 20 \degree \: }}}}$

Now, we got :-

• The Value of x is 20°

Hence,

• The three angles are :-

$\bf \implies \: 2x = 2 \times 20 = { \fcolorbox{orange}{pink}{40 \degree}} \\ \bf \implies \: 3x = 3 \times 20 = { \fcolorbox{orange}{pink}{60 \degree }}\\ \bf \implies4x \: = 4 \times 20 ={ \fcolorbox{orange}{pink}{ 80 \degree}}$

$\mathfrak { \underline{ \green{ \purple V \red e \orange r \pink i \blue c \green a \orange t \red i \purple o \blue n: -}}}$

• Now, verification needs to equal to Solution we have got.

Therefore,

=> Sum of three angles = 180°

=> 2x + 3x + 4x = 180°

=> 40° + 60° + 80° = 180°

=> 180° = 180°

$\bf \therefore L.H.S = R.H.S$

$\mathfrak { \underline{ \green{ Hence,\purple V \red e \orange r \pink i \blue f \green i \red e \pink d : -}}}$