Two angles of a triangle are in the raito 4:5 . If the sum of these an

1.	Two angles of a triangle are in the raito 4:5 . If the sum of these angles is equal to the third angle, find the angles of the triangle
Answer» 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 and third angle = 9x ∘ = 9×10 ∘ =90 ∘

Two angles of a triangle are in the raito 4:5 . If the sum of these angles is equal to the third angle, find the angles of the triangle

Answer»

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

and third angle = 9x

∘

= 9×10

∘

=90

∘