Question

In the figure below , ABCDE is the roof of a house , GB||FD and angle ACE= 106°. Find the angle x​

Answer 1

Answer:

x=53

x=53 because GB||FD AND ACE=106

Answer 2

Given :  ABCDE is the roof of a house

GB||FD and ∠ACE= 106°

To Find :  ∠x

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°)

Method 1 :

Draw a line CP ||  GB and FD

∠BCP = ∠x   and ∠DCP = ∠x   corresponding angles

∠BCP  +  ∠DCP  = ∠BCD = ∠ACE

=> ∠BCP  +  ∠DCP  = 106°

=> x + x =  106°

=> 2x =  106°

=> x =  53°

Hence ∠x is 53°

Another method :

Sum of angles of a pentagon is 540°

∠BGF + ∠DFG = 180°  Supplementary angles  

∠GBC = 180° - x  linear pair

∠FFC = 180° - x  linear pair

=> ∠BGF + ∠DFG + ∠GBC + ∠FFC  + ∠BCD = 540°

∠BCD = ∠ACE  = 106°

=> 180° + 180° - x + 180° - x + 106°  = 540°

=> 2x = 106°

=> x =  53°

Hence ∠x is 53°

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