Question 3: The measures of angles of a triangle are x°, ( x− 20)°, (x− 40)°. Find the measure of each angle.

Question 3:

The measures of angles of a triangle are x°, ( x−$$20)°, (x−$$40)°. Find the measure of each angle.

Answer: 

Let us suppose the angles ∠P, ∠Q, ∠Rof a ∆$$PQR be x°, (x −$$ 20)°, (x −$$ 40)° respectively.
∠P + ∠Q + ∠R = 180∘   (Angle sum property)
⇒ x∘ + (x −$$ 20)° + (x −$$ 40)° = 180∘         
⇒ 3x −$$ 60 = 180  
⇒ 3x = 240
⇒ x ​= 80
Therefore,
∠P = 80∘
∠R = (80 −$$ 20)°
= 60∘
∠R = (80 −$$ 40)°
= 40∘
Hence, the measure of each angle is 80∘, 60∘ and 40∘respectively.