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ABCD is a square. P, Q, R and S are points on the sides AB, BC, CD and DA respectively such that AP = BQ = CR = DS. What is ∠SPQ equal to?

(a) 30° 

(b) 45° 

(c) 60° 

(d) 90°

1 Answer

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Best answer

(d) 90°

In ∆s SAP and PBQ, 

Given

AS = BP 

AP = BQ 

∠A = ∠B = 90° 

∴  ∆SAP ≅ ∆PBQ                (SAS) 

⇒ SP = PQ 

∠SPA = ∠BQP = x (say) 

and ∠PSA = ∠QPB = y (say) 

In ∆SAP or ∆PBQ x + y = 90°

∴ ∠SPQ = 180° – (∠SPA + ∠BPQ) = 180° – ( x + y) = 180° – 90° = 90°

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