From the given figure,
4x and 2y +x are supplementary angles
Supplementary angles are added upto 180 degrees
So 4x + 2y +x = 180
5x + 2y = 180 -------------> equation 1
4x and 2y-x are vertical angles so they are equal
4x = 2y - x
Keep all the x and y terms on left hand side
add x and subtract 2y on both sides
5x - 2y =0 -------- > equation 2
Add equations 1 and 2
5x + 2y = 180
5x - 2y = 0
10 x = 180 ( divide by 10 on both sides)
x= 18
