In a ∆ABC, ∠A = x°, ∠B = 3x° and ∠C = y°. If 5x – 3y + 30

1.	In a ∆ABC, ∠A = x°, ∠B = 3x° and ∠C = y°. If 5x – 3y + 30 = 0, then prove that it is a right angled triangle.
Answer» Since it is given that ∠A = x°, ∠B = 3x° and ∠C = y°. ∠A + ∠B + ∠C = 180° (by angle sum property of a triangle) ⇒ x + 3x + y = 180° ⇒ 4x + y = 180° …..(i) Also 5x – 3y + 30 = 0 ⇒ 5x – 3y = -30 …(ii) Multiply equation (i) by 3 to make coefficient of y equal and then adding with (ii), we get 17x = 510 ⇒ x = 30° Now putting the value of x in equation (i), we get 4 x 30° + y – 180° or y = 180° – 120° or y = 60° Sum of two angles x and y is 90° Hence, it is a right angled triangle.

In a ∆ABC, ∠A = x°, ∠B = 3x° and ∠C = y°. If 5x – 3y + 30 = 0, then prove that it is a right angled triangle.

Answer»

Since it is given that

∠A = x°, ∠B = 3x° and ∠C = y°.

∠A + ∠B + ∠C = 180° (by angle sum property of a triangle)

⇒ x + 3x + y = 180°

⇒ 4x + y = 180° …..(i)

Also 5x – 3y + 30 = 0

⇒ 5x – 3y = -30 …(ii)

Multiply equation (i) by 3 to make coefficient of y equal and then adding with (ii), we get

17x = 510 ⇒ x = 30°

Now putting the value of x in equation (i), we get

4 x 30° + y – 180°

or y = 180° – 120°

or y = 60°

Sum of two angles x and y is 90°

Hence, it is a right angled triangle.