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In Fig, if AB || CD || EF, PQ || RS, ∠RQD = 25 . . .

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.