Call F₁ is an exterior angle 

 and F₂ is an adjacent angle 

We have :

F₁ + F₂ = 180⁰ ( 2 adjacent offset angle )

=> F₂ = 180⁰ - 5x - 34⁰ = 146⁰ - 5x

Consider triangle DEF , we have :

F₂ + D + E = 180⁰ - 5x + 2x + 5⁰ + 4x + 20⁰ = 180⁰

<=> 205⁰ + x = 180⁰

=> x = 205⁰ - 180⁰

=> x = 25⁰