In fig. TQ and TR are bisectors of ∠Q and ∠R respectively. If ∠QPR = 80∘ and ∠PRT = 30∘. Determine ∠TQR. [4 MARKS]
Concept : 1 Mark
Process : 2 Marks
Result : 1 Mark
Since the bisectors of ∠Q and ∠R meet at T.
∠QTR = 90∘ + 12∠QPR [By Corollary]
⇒ = 90∘ + 12×80∘
⇒∠QTR = 130∘
In ΔQTR, we have
∠TQR + ∠QTR + ∠TRQ = 180∘
⇒ ∠TQR + 130∘ + 30∘ = 180∘
⇒ ∠TQR = 20∘