Question

12) Two angles of a triangle are in the ratio 4: 5. If the sum of these an
is equal to the third angle. Find the angles of the triangle?​

Answer 1

Answer:

Let the two angles of the triangle be 4x and 5x.

Then, as per the question, we know

third angle =4x+5x=9x

We know that sum of all the angles of a triangle is 180 ∘

.

∴4x+5x+9x=180 ∘

⇒18x=180 ∘

⇒x=10 ....[On dividing both sides by 18]

So, first angle = 4x ∘ = 4×10 ∘ =40 ∘

,second angle = 5x ∘ = 5×10 ∘ =50 ∘

and third angle = 9x ∘ = 9×10 ∘ =90 ∘

Answer 2

$\large\mathfrak \pink{Solution:-}$

$\underline \mathbb{GIVEN:-}$

The figure is a triangle.

Ratio of  the two angles = 4 : 5

Sum of the two angles is equal to the third angle .

$\underline \mathbb{TO  \: FIND:-}$

The value of all the angles.

$\underline \mathbb{FORMULA:-}$

Sum of all the three angles of a triangle = 180°

$\underline \mathbb{ASSUMPTION:-}$

Let, the 1st angle be 4x

2nd angle be 5x

3rd angle be 4x + 5x = 9x (Sum of the two angles)

$\underline \mathbb{BY  \: THE  \: PROBLEM:-}$

4x + 5x + 9x = 180°

or, 18x = 180°

or, x = $\cancel\frac{180°}{18}$

or, x = 10°

$\underline \mathbb{ANSWER:-}$

1st angle = 4x = 4×10° = 40°

2nd angle = 5x = 5×10° = 50°

3rd angle =  9x = 9×10° = 90°(40° + 50°)