Question

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

Answer 1

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.