In figure, side QR of Δ PQR has been produced to S. If ∠ P : ∠ Q : ∠ R = 3 : 2 : 1 and RT ⊥ PR, find ∠ TRS.
    

Given: In Δ PQR, ∠ P : ∠ Q : ∠ R = 3 : 2 : 1.
RT ⊥ PR, then ∠ PRT = 90°
To find: ∠ TRS
Proof:
In Δ PQR,
∠ P + ∠ Q + ∠ R = 180° [Sum of the three angles of a Δ is 180° ]
Ratio of the angles of the Δ PQR = ∠ P : ∠ Q : ∠ R = 3 : 2 : 1
                                    ∴ ∠ R =× 180° = 30°
Now, ∠ PRQ + ∠ PRT + ∠ TRS = 180°   [Linear pair axiom]
           ⇒ 30° + 90° + ∠ TRS = 180°
                            ⇒ ∠ TRS = 180° - (30° + 90° )
                                         = 180° - 120°
                                         = 60°