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In the given figure, ΔQPS ≅ ΔSRQ. Find the measure of ∠PSR.  

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SSC CGL 2023 Tier-I Official Paper (Held On: 21 Jul 2023 Shift 1)
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  1. 64°
  2. 74°
  3. 52°
  4. 82°

Answer (Detailed Solution Below)

Option 2 : 74°
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Detailed Solution

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Given

ΔQPS ≅ ΔSRQ

Concept used

Congruency: Two triangles are said to be congruent if they have all their corresponding sides and angles equal to each other

Calculation

According to the question,

∠P = ∠R
 
⇒ 106 = 2x + 12
 
⇒ 2x = 94
 
⇒ x = 94/2 = 47
 
∠QSR = 180 - 52 - 106 = 22
 
∠PSQ = ∠SQR = 52
 
∠S = 52 + 22 = 74°
 
The answer is 74°.
 

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