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in Lines and Angles by (47.3k points)
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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°

1 Answer

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Best answer

(c) 145°

Given, PQ || RS

∠PQC = ∠BRS = 60° [alternate exterior angles and

∠PQC = 60° (given)] and ∠DQR = ∠QRA = 25° [alternate interior angles]

[∠DQR = 25°, given]

∠QRS = ∠QRA + ∠ARS

= ∠QRA + (180° – ∠BRS) [linear pair axiom]

= 25° + 180° – 60°

= 205° – 60°

= 145°

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