In the given figure, EF||DQ and AB||CD. If angle FEB = 64° and angle PDC = 27°, then find angle PDQ, angle AED and angle DEF.
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In the given figure, EF||DQ and AB||CD. If angle FEB = 64° and angle PDC = 27°, then find angle PDQ, angle AED and angle DEF.
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Verified answer
Answer:
•angle PDQ = 89°
Step-by-step explanation:
•angle AED = 27°
•angle DEF = 89°
Given : EF||DQ and AB||CD.
∠FEB = 64° and ∠PDC = 27°,
To Find : ∠PDQ, ∠AED and ∠DEF.
Solution:
Properties of angles formed by transversal line with two parallel lines :
• Corresponding angles are congruent. ( Equal in Measure)
• Alternate angles are congruent. ( Interiors & Exterior both )
• Co-Interior angles are supplementary. ( adds up to 180°)
AB||CD and PE is transversal
∠AED = ∠CDP Corresponding angles
∠CDP = ∠PDC = 27°,
=> ∠AED = 27°
AB is straight line
=> ∠AED + ∠DEF + ∠FEB = 180°
=> 27° + ∠DEF + 64° = 180°
=> ∠DEF = 89°
EF || DQ and PE is transversal
∠PDQ = ∠DEF Corresponding angles
=> ∠PDQ = 89°
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