Question

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.​

Answer 1

Answer:

•angle PDQ = 89°

Step-by-step explanation:

•angle AED = 27°

•angle DEF = 89°

Answer 2

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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