We know that, in a triangle , the sum of three angles is 180°
∴ ∠A + ∠B + ∠C = 180°
According to the question,
x + 3x + y = 180
⇒ 4x + y = 180
⇒ y = 180 – 4x …(i)
Given that 3y — 5x = 30 …(ii)
On substituting the value of y in Eq. (ii), we get
3(180 – 4x) – 5x = 30
⇒ 540 – 12x – 5x = 30
⇒ 540 – 17x = 30
⇒ – 17x = 30 – 540
⇒ – 17x = – 510
⇒ x = 30
Now, we substitute the value of x in Eq.(i), we get
⇒ y = 180 – 4(30)
⇒ y = 60
On putting the value of x and y, we calculate the angles
∠A = x° = 30°
∠B = (3x)° = 3(30) = 90°
and ∠C = y° = 60°
Here, we can see that ∠B = 90° , so triangle is a right angled.