Question

In the given figure, ∠QPR = 50° and ∠PQR = 60°. Show that: SN < SR

Answer 1

In ΔRTQ,
∠RTQ + ∠TQR + ∠TRQ = 180°
90° + 60° +∠TRQ = 180°
150° + ∠TRQ = 180°
∠TRQ = 180° - 150°
∠TRQ = 30°
∠TRQ = ∠SRN = 30°    ....(i)
In NSR,
∠RNS + ∠SRN = 90°  ....(∵∠NSR = 90°)
∠RNS + 30° = 90°      ....[from (iii)]
∠RNS = 90° - 30°
∠RNS = 60°               ....(ii)
∠SRN < ∠RNS          ....(from (iii) and (iv))
SN < SR.