Question

If the angles of the triangle are in ratio 2:3:4 . Find all the tree angles of the triangle

Answer 1

Given :-

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

To Find :-

• All the Three angles of the Triangle

Solution :-

⟼ Let the First angle be 2x

⟼ Let the Second angle be 3x

⟼ Let the Third angle be 4x

❏ As we know that, Sum of all the angles of a Triangle is 180° ( Angle sum Property ).

According to the Question :

➞ ∠1 + ∠2 + ∠3 = 180

➞ 2x + 3x + 4x = 180

➞ 5x + 4x = 180

➞ 9x = 180

➞ x = 180 / 9

➞ x = 20

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Verification :-

⟾ ∠1 + ∠2 + ∠3 = 180

⟾ 2x + 3x + 4x = 180

⟾ 2 × 20 + 3 × 20 + 4 × 20 = 180

⟾ 40 + 60 + 80 = 180

⟾ 100 + 80 = 180

⟾ 180 = 180

Hence Verified

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Therefore :

➟ First Angle = 2x = 2 × 20 = 40°

➟ Second Angle = 3x = 3 × 20 = 60°

➟ Third Angle = 4x = 4 × 20 = 80°

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Answer 2

Given :

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

To Find :

✰ All angles of triangle

Solution :

✰ As we know that sum of all angles of triangle is 180°. Angles of traingle are given in ratio 2:3:4. So, we will let the first angle be 2y, second angle be 3y and the third angle 4y. Firstly we will find the value of y and then Put value of y in the given angles

Let the required Angles be ∠A,∠B and ∠C

Where,

• First angle ∠A = 2y

• Second angle∠B = 3y

• Third angle ∠C = 4y

∠A + ∠B + ∠C = 180°

➣ 2y + 3y + 4y = 180°

➣ 5y + 4y = 180

➣ 9y = 180

➣ y = 180/9

➣ y = 20

The Required angles are

• 2y = 2 × 20 = 40°

• 3y = 3 × 20 = 60°

• 4y = 4 × 20 = 80°

∴ The Angles are 40°, 60° and 80°