Question

14. The angles of a triangle ABC are in the ratio 2:3:4. Find the largest angle of the triangle.​

Answer 1

Answer :-

• The largest angle of triangle is 80°.

Step-by-step explanation :-

To Find :-

• The largest angle of triangle

Solution :-

Given that,

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

Assumption: Let us assume the unknown ratio angles of triangle as 2x, 3x and 4x, and we know that, Sum of all Interior angles of a triangle = 180°,

Therefore,

• 2x + 3x + 4x = 180°

=> 2x + 3x + 4x = 180

=> 5x + 4x = 180

=> 9x = 180

=> x = 180/9

=> x = 20

The value of x is 20.

Now, the angles of triangle are :-

• The angle which we assumed as 2x

=> 2x

=> 2*20

=> 40°

• The angle which we assumed as 3x

=> 3x

=> 3*20

=> 60°

• The angle which we assumed as 4x

=> 4x

=> 4*20

=> 80°

Hence, The measure of all the angles of triangle are 40°, 60° and 80°.

According the question,

• The largest angle is,

=> 80 > 60 > 40

So, The largest angle of triangle is 80° [ 4x ].

Answer 2

Given :-

• Shape = Triangle
• The angles of a triangle ABC are in the ratio 2:3:4.

To Find :-

• The largest angle of the triangle.

Solution :-

Let the First Angle be 2x

Let the Second Angle be 3x

Let the Third Angle be 4x

★ Angle Sum Property of Triangle is 180° ★

According to the Question :-

➞ ∠1 + ∠2 + ∠3 = 180

➞ 2x + 3x + 4x = 180

➞ 5x + 4x = 180

➞ 9x = 180

➞ x = 180/9

➞ x = 20

________________

Therefore :-

• First Angle = 2x = 2 × 20 = 40°
• Second Angle = 3x = 3 × 20 = 60°
• Third Angle = 4x = 4 × 20 = 80°

________________

So, the Largest Angle of the Triangle is third i.e 80°

________________