Hello from MrBillDoesMath!
Answer:
x = 16, y = 20
Discussion:
Assuming the lines shown are parallel, corresponding angles are equal which gives:
6x + y = x + 5y => (subtract "y" from each side)
6x = x + 4y => (subtract "x" from each side)
5x = 4y (A)
As there are 180 degrees in a line we also have
4x + (6x + y) = 180 =>
10x + y = 180 => (subtract 180 from each side)
y = 180 - 10x
y = 180 - 2 *(5x) => (Using (A) above )
y = 180 - 2(4y) => (Add 8y to each side)
y + 8y = 180 =>
9y = 180 =>
y = 180/9 = 20
As 5x = 4y, 5x = 4(20), or 5x = 80, or x = 80/5 = 16
Thank you,
MrB