Question

In a triangle the largest angle is 5° more than 4 times the smallest. The 3rd angle is twice the smallest angle. Find the smallest angle? ​

Answer 1

✬ Smallest Angle = 25° ✬

Step-by-step explanation:

Given:

• Largest angle is 5° more than 4 times the smallest.
• Third angle is twice the smallest angle.

To Find:

• What is the smallest angle ?

Solution: Let the smallest angle be x°. Therefore,

➟ Largest angle of ∆ = 5 more than 4x

➟ Largest angle = (4x + 5)°

➟ Third angle = 2 times of x = 2x°

Here we got

• First angle = x°
• Second angle = (4x + 5)°
• Third angle = 2x°

As we know that

★ Sum of all angles of ∆ = 180° ★

$\implies{\rm }$ x° + 4x + 5 + 2x° = 180°

$\implies{\rm }$ 5x° + 2x° = 180° – 5°

$\implies{\rm }$ 7x° = 175°

$\implies{\rm }$ x° = 175°/7°

$\implies{\rm }$ x° = 25°

So angles of triangle are

• Smallest angle = 25°

• Largest angle = 4 × 25 + 5 = 105°

• Second angle = 2 × 25 = 50°

Answer 2

Given

• The largest angle is 5° more than 4 times the smallest.
• The 3rd angle is twice the smallest angle.

To find

• Smallest angle

Solution

⇝ Let the smallest angle of triangle be x.

Then,

⇝ Largest angle = (5 + 4x)°

⇝ Third angle = 2x

We know that

$\underline{\boxed{Angle\: sum\: property\: of\: a\: triangle = 180°}}$

According to the question

→ x + 2x + (5 + 4x) = 180

→ 7x + 5 = 180

→ 7x = 180 - 5

→ 7x = 175

→ x = 25

Therefore,

⟹ Smallest angle = 25°

⟹ Largest angle = (5 + 4x)°

⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀ = 5 + 100

⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀ = 105°

⟹ Third angle = 2x

⠀⠀⠀⠀⠀⠀⠀⠀⠀ = 50°