Question

If the ratios of the three angles of a triangle are 2: 3: 4 then look at the smallest angle.​

Answer 1

Given :-

Ratio of side = 2:3:4

To Find :-

Smallest angle

Solution :-

Let the angle be 2x, 3x and 4x

Sum of all angle in a triangle = 180

2x + 3x + 4x = 180

9x = 180

x = 180/9

x = 20

2x = 2(20) = 40°

3x = 3(20) = 60°

4x = 4(20) = 80°

Smallest angle = 40°

Answer 2

Answer:

Given :-

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

To Find :-

• What is the smallest angle.

Solution :-

Let,

◘ First angle = 2x

◘ Second angle = 3x

◘ Third angle = 4x

As we know that,

✪ Sum of angles of a triangle = 180° ✪

According to the question by using the formula we get,

⇒ 2x + 3x + 4x = 180°

⇒ 5x + 4x = 180°

⇒ 9x = 180°

⇒ x = 180°/9

⇒ x = 20°/1

➠ x = 20°

Hence, the required angles of a triangle are :

➲ First angle of a triangle :

↦ 2x

↦ 2(20°)

↦ 2 × 20°

➦ 40°

➲ Second angle of a triangle :

↦ 3x

↦ 3(20°)

↦ 3 × 20°

➦ 60°

➲ Third angle of a triangle :

↦ 4x

↦ 4(20°)

↦ 4 × 20°

➦ 80°

∴ The smallest angle of a triangle is 40°.

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VERIFICATION :-

↦ 2x + 3x + 4x = 180°

By putting x = 20° we get,

↦ 2(20°) + 3(20°) + 4(20°) = 180°

↦ 40° + 60° + 80° = 180°

➤ 180° = 180°

Hence, Verified.