Question

In Figure AB||CD, EF||DQ. Determine the measures of Angle PDQ, Angle AED and Angle DEF.​

Answer 1

$\huge\mathbb\fcolorbox{purple}{lavenderblush}{Solution:-}$

∵ 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°

Answer 2

∵ 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