Question

In a ABC, ∠A = x°, ∠B = (2x - 30)°, ∠C = y° and also, ∠A + ∠B = one right angle. Find the angles. Also, state the type of this triangle.

Answer 1

In ΔABC,
∠A = x°, ∠B = (2x - 30)°, ∠C = y° 
Now, sum of the angles of a triangle is 180°.
⇒ ∠A + ∠B + ∠C = 180°
⇒ x° + (2x - 30) + y = 180°
⇒ 3x° + y° = 210°    ....(i)
Also, it is given that ∠A + ∠ B = 90°
⇒ x° + (2x - 30)° = 90°
⇒ 3x° = 120°
⇒ x° = 40° = ∠A
⇒ ∠B = 2(40°) - 30°
= 80° - 30°
= 50°
Substituting the value of x in eqn. (i), we  get
⇒  3(40°) + y° = 210°
⇒  120° + y° = 210°
⇒  y °= 90° = ∠C
Thus, the three angles of a triangle are as follows :
∠A = 40°, ∠B = 50° and ∠C = 90°
It is a right- angled triangle right angle at C.