Answer:
The value of x is [tex]31^{\circ}[/tex].
Step-by-step explanation:
Please look at the figure attached to get more clear solution.
We have given:
FG||CB
And the line that cut the parallel line is transversal so, here BA is transversal
And alternate interior angles on transverse line are equal
So, ∠1=∠4
And ∠4=[tex]28^{\circ}[/tex]
Hence, ∠1=∠4=[tex]28^{\circ}[/tex]
And On FG the sum of angles will be [tex]180^{\circ}[/tex]
∠3+∠2+∠1=[tex]180^{\circ}[/tex]
[tex]90^{\circ}[/tex]+∠2+[tex]28^{\circ}[/tex]=[tex]180^{\circ}[/tex]
Hence, ∠2=[tex]62^{\circ}[/tex]
Now, we know that the sum of interior angles is equal to the exterior angle:
Therefore, ∠2+∠5=∠6+∠7
[tex]62^{\circ}+3x=x+4x[/tex]
On simplification we get:
[tex]2x=62^{\circ}[/tex]
[tex]x=31^{\circ}[/tex]
Hence, the value of x is [tex]31^{\circ}[/tex].
