Looking at the given diagram, line l is parallel to line m and a transversal cuts through both lines. Also, angle (6y + 29) and angle (8x + 1) are linear pairs. They lie on a straight line. Recall, the sum of the angles on a straight line is 180 degrees. This means that
6y + 29 + 8x + 1 = 180
8x + 6y = 180 - 29 - 1
8x + 6y = 180 - 30
8x + 6y = 150 equation 1
Again,
The angle vertically opposite angle 10x - 17 can be represented by x as shown in the diagram below. The angle vertically opposite angle 8x + 1 is also represented by y.
Vertically opposite angles are equal. this means that angle x = 10x - 17. This also means that y = 8x + 1
Also, angle x and angle y are alternate external angles because the lie on opposite sides of the transversal and outside the parallel lines. Alternate angles are equal. It means that
10x - 17 = 8x + 1
10x - 8x = 1 + 17
2x = 18
x = 18/2
x = 9
Substituting x = 9 into equation 1, it becomes
8 * 9 + 6y = 150
72 + 6y = 150
6y = 150 - 72 = 78
y = 78/6
y = 13
x = 9, y = 13