Given:
A figure.
To find:
The value of x.
Solution:
Draw two parallel lines as shown in the below figure.
If a transversal line intersect two parallel lines, then alternate interior angles are same.
[tex]a=20[/tex] (Alternate interior angle)
[tex]d=b[/tex] (Alternate interior angle) ...(i)
The value of angle d is
[tex]d=50-a[/tex]
[tex]d=50-20[/tex]
[tex]d=30[/tex]
Using (i), we get
[tex]b=30[/tex]
If a transversal line intersect two parallel lines, then same sides interior angles are supplementary angles.
[tex]c+140=180[/tex]
[tex]c=180-140[/tex]
[tex]c=40[/tex]
Now,
[tex]x=b+c[/tex]
[tex]x=30+40[/tex]
[tex]x=70[/tex]
Therefore, the value of x is 70.
