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
