In the given figure if l₁//l_2,a₁//a₂ ​find the value of x.​

Dear Student,

Please find below the solution to the asked query:

Given l₁  | | l₂   and a₁  | | a₂

We form our diagram , As :

Here ,

$\angle$ ABC  = $\angle$ BDE                                      ( Corresponding Angles , As a₁  | | a₂ and l₁ is transversal line )

$\angle$ BDE  = 2x                                              ( Given $\angle$ ABC  = 2x )

And


$\angle$ BDE + $\angle$ FDE  = 180$°$                        ( Linear pair angles )

2x + $\angle$ FDE  = 180$°$                  

$\angle$ FDE  = 180$°$  - 2x                              --- ( 1 )

And

$\angle$ FDE  = $\angle$ GEH                                      ( Corresponding Angles , As l₁  | | l₂ and a₂ is transversal line )

180$°$  - 2x = 4 x  - 30                                             ( From equation 1 and As given  $\angle$ GEH  = 4 x  - 30 )

6 x  = 210$°$ 

x  =  35$°$                                                                ( Ans )

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