Question : In Fig, if AB || CD || EF, PQ || RS, ∠RQD = 25° and ∠CQP = 60°, then ∠QRS is equal to
(A) 85°
(B) 135°
(C) 145°
(D) 110°
Doubt by veer
Solution :
AB || CD || EF (Given)
∠RQD = 25° and ∠CQP = 60° (Given)
∠QRS=?
∠ARQ=∠RQD =25° [Alternate Interior Angles]
∠ARQ=25° — (1)
∠CQP=∠SRB=60° [Alternate Exterior Angles]
∠SRB=60°
Now,
∠SRB + ∠SRA = 180° [Linear Pair]
60° + ∠SRA = 180°
∠SRA=180°-60°
∠SRA=120° — (2)
Adding equation (1) and (2)
∠ARQ+∠SRA=25°+120°
∠QRS = 145°
Hence, (C) 145°, would be the correct option.