In a ΔABC, ∠A = x°, ∠B = (3x)° and ∠C = y°.
If 3y — 5x = 30, show that the triangle is right – angled.

Question

In a ΔABC, ∠A = x°, ∠B = (3x)° and ∠C = y°.If 3y — 5x = 30, show that the triangle is right – angled.

Philoid · Accepted Answer

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.