Question

If the angles of a triangle are in the ratio 2 : 3 : 4. Find the three angles.​

Answer 1

$\huge\fbox\orange{QUE}{\colorbox{blue}{ST}}\fbox\green{ION}$

If the angles of a triangle are in the ratio 2 : 3 : 4. Find the three angles.

$\huge{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$

$\sf\green{Given :}$

➣ The three angles of a triangle are in the ratio 2 : 3 : 4

$\sf\red{To \: Find :}$

➣ The measure of all the three angles of a triangle

$\sf\pink{Solution :}$

➪ Let, the first angle of the triangle = 2x

➪ Let, the second angle of the triangle = 3x

➪ Let, the third angle of the triangle = 4x

⇒ By using Angle Sum Property of Triangle

⇒ Sum of Angles in a triangle = 180°

⟼ 2x + 3x + 4x = 180°

⟼ 9x = 180°

⟼ x = $\cancel\frac{180}{9}$

⟼ x = 20°

➙ The Measure of the first angle of the triangle = 2x = 2 × 20 = 40°

➙ The Measure of the second angle of the triangle = 3x = 3 × 20 = 60°

➙ The Measure of the third angle of the triangle = 4x = 4 × 20 = 80°

➦ So, the three angles of the triangle are 40°, 60° and 80°.

Answer 2

Answer:

• The angles in the triangle are 20 , 60 , 80 degrees respectively

Given:

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

To Find:

• The measure of the three angles

Assumptions:

• Let the 1st angle of the triangle be 2x
• Let the 2nd angle of the triangle be 3x
• Let the 3rd angle of the triangle be 4x

According to the question:

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

$\longmapsto \sf 5x + 4x = 180$

$\longmapsto \sf 9x = 180$

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

$\longmapsto \sf {\purple{\underline{\boxed{\frak{x=20}}}}}$    

HENCE,

• 1st angle of the triangle = 2x = 2(20) = 40°
• 2nd angle of the triangle = 3x = 3(20) = 60°
• 3rd angle of the triangle = 4x = 4(20) = 80°

Verification:

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

$\longrightarrow \sf 40 + 60 + 80 = 180$

$\longrightarrow \sf 100 + 80 = 180$

$\longmapsto \sf {\purple{\underline{\boxed{\frak{180 = 180}}}}}$

Therefore:

• The angles in the triangle are 20 , 60 , 80 degrees respectively

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━