In a ΔABC, ∠A = x°, ∠B = 3x°, ∠C = y°. If 3y – 5x = 30, pr

1.	In a ΔABC, ∠A = x°, ∠B = 3x°, ∠C = y°. If 3y – 5x = 30, prove that the triangle is right angled.
Answer» We need to prove that ΔABC is right angled. Given: ∠A = x°, ∠B = 3x° and ∠C = y° Sum of the three angles in a triangle is 180° (Angle sum property of a triangle) i.e., ∠A + ∠B + ∠C = 180° x + 3x + y = 180° 4x + y = 180 —— (i) From question it’s given that, 3y – 5x = 30 —– (ii) To solve (i) and (ii), we perform Multiplying equation (i) by 3 to get, 12x + 36y = 540 —– (iii) Now, subtracting equation (ii) from equation (iii) we get 17x = 510 x = 510/17 ⇒ x = 30° Substituting the value of x = 30° in equation (i) to find y 4x + y = 180 120 + y = 180 y = 180 – 120 ⇒ y = 60° Thus the angles ∠A, ∠B and ∠C are calculated to be ∠A = x° = 30° ∠B = 3x° = 90° ∠C = yo = 60° A right angled triangle is a triangle with any one side right angled to other, i.e., 90° to other. And here we have, ∠B = 90°. Therefore, the triangle ABC is right angled. Hence proved.

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

Answer»

We need to prove that ΔABC is right angled.

Given:

∠A = x°, ∠B = 3x° and ∠C = y°

Sum of the three angles in a triangle is 180° (Angle sum property of a triangle) i.e.,

∠A + ∠B + ∠C = 180°

x + 3x + y = 180°

4x + y = 180 —— (i)

From question it’s given that,

3y – 5x = 30 —– (ii)

To solve (i) and (ii), we perform

Multiplying equation (i) by 3 to get,

12x + 36y = 540 —– (iii)

Now, subtracting equation (ii) from equation (iii) we get

17x = 510

x = 510/17

⇒ x = 30°

Substituting the value of x = 30° in equation (i) to find y

4x + y = 180

120 + y = 180

y = 180 – 120

⇒ y = 60°

Thus the angles ∠A, ∠B and ∠C are calculated to be

∠A = x° = 30°

∠B = 3x° = 90°

∠C = yo = 60°

A right angled triangle is a triangle with any one side right angled to other, i.e., 90° to other.