Question

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

Answer 1

Answer:

Let the angles be = 2x,3x,4x

$\color{black}\boxed{\colorbox{saffron}{Perimeter-sum\:of\:sides}}$

2x+3x+4x=180° (angle sum property)

$2x + 3x + 4x = 180 \\ \\9 x = 180 \\ \\ = x = 20$

So,

$\rightarrow$2x= 40°

$\rightarrow$3x= 60°

$\rightarrow$4x=80°

Answer 2

↔Question:  If the angles of a triangle are in the ratio 2:3:4. Find the measure of each angle​?

⇔Given: Angles of Triangle in the ratio = 2:3:4

⇔ Let the angles be 2x , 3x , 4x   ( where x is any value)

⇔To find: Measure of each angle.

⇒We, know that sum of (interior) angles in a triangle will be equal to 180° which is called angle sum property.

↔ 2x+3x+4x = 180°

↔ 9x = 180°

↔ x = 180÷9

↔ x =20

∴ x =20

⇔Now, let's substitute the values in :

• 2x = 2×20 = 40°
• 3x = 3×20 = 60°
• 4x = 4×20 = 80°

∴The measure of each angle in the triangle are 40°, 60°, 80°.

⇄Verify⇆

The sum of all the angles will be equal to 180°

40°+60°+80° = 180°

180° = 180°

∴ We can conclude that the measure of each angle in the triangle are 40°, 60°, 80°.