In ΔPQR, ∠P = 120°, PS ⊥ QR at S and PQ + QS = SR, then the measured value of ∠PTQ is ?
Answer & explanation
Correct answer: option 2
Draw a line PT such that QS = ST
Step 1:
In ΔQPT
QS = ST and PS ⊥ QT
the ΔQPT is isosceles triangle then PQ = PT
Step 2:
As PQ = PT so ∠Q = ∠T = 2θ
and PT = TR ⇒ ∠TPR = ∠TRP = θ
In ΔPQR
∠P + ∠Q + ∠R = 180° (∠P = 120°)
3θ = 60°
θ = 20°
∠PTQ = 2 × 20° = 40°