Question

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

Answer 1

GIVEN :

• Measures of angles of a triangle are in the ratio = 2 : 3: 4

TO FIND :

• The measure of each angle.

SOLUTION

As we know that in a triangle :

• $\underline {\boxed{\bf Sum\:of\:angles =180^{\circ}}}$

Let the measures of angles be (2x)°, (3x)°, and (4x)°.

Substitute the given values in the formula :

$\longrightarrow\sf 2x+3x+4x=180$

$\longrightarrow\sf 9x=180$

$\longrightarrow\sf x=\cancel {\dfrac {180}{9}}$

$\longrightarrow\underline{\boxed{\bf x=20}}$

Measure of each angle :

▪$\longrightarrow\tt (2x)^{\circ}=2\times 20 =40^{\circ}$

▪$\longrightarrow\tt (3x)^{\circ}=3\times 20 =60^{\circ}$

▪$\longrightarrow\tt (4x)^{\circ}=4\times 20 =80^{\circ}$

Answer 2

Given : Ratio of the measure of the angles of a triangles = 2 : 3 : 4

To Find : The measure of each angles of the triangle ?

__________________________

❍ Let's consider the ratio 2 : 3 : 4 as 2x : 3x : 4x

$~$

• Sum of measures of all sides of a triangle - 180°

$~$

So, We can say,

$~~~~~~~~~~{\sf:\implies{2x~+~3x~+~4x~=~180^\circ}}$

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

$~~~~~~~~~~{\sf:\implies{x~=~\dfrac{180}{9}}}$

$~~~~~~~~~~{\sf:\implies{x~=~\cancel\dfrac{180}{9}}}$

$~~~~~~~~~~:\implies{\sf{x~=~20}}$

$~~~~~~~~~~:\implies\underset{\blue{\rm Required\ Answer}}{\underbrace{\boxed{\frak{\pink{Measure~of~x~is~20}}}}}$

$~$

Therefore,

• The measure of all the sides of the triangle is in the ratio would be :

$~$

• (20 × 2) : (20 × 3) : (20 × 4)

• 40 : 60 : 80

$~$

• ${\sf:\leadsto{20~×~2~=~40^\circ}}$

• ${\sf:\leadsto{20~×~3~=~60^\circ}}$

• ${\sf:\leadsto{20~×~4~=~80^\circ}}$

$~$

$\therefore\underline{\sf{The~measure~of~the~three~angles~of~the~triangle~is~\bf{40^\circ},\bf{60^\circ}~\&~\bf{80^\circ}}}$