Find the value of x and the value of y. a. x = 15, y = 10 b. x = 20, y = 50 c. x = 50, y = 10 d. x = 50, y = 20

x = 50
y = 10

Explanation:
When two lines intersect, four angles are formed. A theorem states that each two vertically opposite angles are equal.

Applying this on the given, we would find that:
1) 3y and x-20 are vertically opposite angles. This means that:
3y = x - 20
This can be rewritten as:
x = 3y + 20 > equation I
2) y+140 and 5x-100 are vertically opposite angles. This means that:
y + 140 = 5x - 100 > equation II

Substitute with I in II and solve for y as follows:
y + 140 = 5x - 100
y + 140 = 5(3y+20) - 100
y + 140 = 15y + 100 - 100
15y - y = 140
14y = 140
y = 10

Substitute with the value of y in equation I to get x as follows:
x = 3y + 20
x = 3(14) + 20
x = 50

Hope this helps :)

X - 20 + 5x - 100 = 180
6x - 120 = 180
6x = 300
  x = 50

3y = x - 20
3y = 50 -20
3y = 30
y = 10

answer
C. x = 50 and y = 10