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In the given figure, if AB || CD and EF || DQ, then find the value of angles ∠PDQ, ∠AED and ∠DEF.

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∵ AB || CD and transversal line intersect E and D respectively. 

∴ ∠AED = ∠CDP (corresponding angles) 

=> ∠AED = 34° 

Ray EF is inclined on line AB at point E 

∴ ∠AEF + ∠BEF = 180° 

=> (∠AEP + ∠PEF) + ∠BEF = 180° [ ∵ ∠AEF = ∠AEP + ∠PEF] 

=> 34° + ∠PEF + 78° = 180° 

=> ∠PEF = 180°- 112° = 68° 

=> ∠DEF = 68° …(1) 

∵ EF || DQ and transversal line DE intersects at E and D respectively. 

∵ ∠FED = ∠PDQ = 68° [ ∵ ∠FED = ∠PEF = 68°] 

=> ∠PDQ = 68° 

So ∠PDQ = ∠DEF = 68°, ∠AED = 34°

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