In triangle PQR ∠P=55° and QR =18 cm. in which of the following cases, ∆PQR can be an obtuse scalene triangle?

Correct option is A

Option (a): If ∠R=15°, then ∠Q = 180° - (∠P + ∠R) = 180° - (55° + 15°) = 110°, making ∠Q an obtuse angle. PR being greater than 18 cm does not contradict the requirements for a scalene triangle.
Option (b) If ∠R=55°, then ∠Q = 180° - (55° + 55°) = 70°, making all angles acute.
Option (c) If ∠R=35°, then ∠Q = 180° - (55° + 35°) = 90°, making ∠Q a right angle, not obtuse.
Option (d) If ∠R=25°, then ∠Q = 180° - (55° + 25°) = 100°. While this results in an obtuse angle, specifying PQ=18cm and knowing QR=18cm contradicts the requirement for a scalene triangle since it implies two sides are of equal length.