Answer:
Without a diagram or additional context, it's difficult to determine the values of x and y precisely. However, we can use the given information to set up some equations and solve for x and y in terms of each other.
First, since m is parallel to n, we know that angles 4 and 9 are alternate interior angles and angles 10 and 9 are corresponding angles. Therefore:
angle 4 = angle 9 (alternate interior angles)
angle 9 + angle 10 = 180 degrees (interior angles on the same side of the transversal)
angle 4 + angle 10 = 180 degrees (corresponding angles)
Substituting the given expressions for each angle, we have:
6x - 5 = 3y - 10
5x + 8 + 3y - 10 = 180
6x - 5 + 5x + 8 = 180
Simplifying the second equation by combining like terms, we get:
8x + 3y - 2 = 0
We can now solve for one variable in terms of the other. From the first equation, we have:
6x = 3y + 5
x = (3/2)y + (5/6)
Substituting this expression for x into the third equation, we get:
6((3/2)y + (5/6)) - 5 + 5((3/2)y + (5/6)) + 8 = 180
Simplifying and solving for y, we get:
y = 29/9
Substituting this value for y back into the expression we found for x, we get:
x = (3/2)(29/9) + (5/6) = 59/6
Therefore, the values of x and y that satisfy the given conditions are x = 59/6 and y = 29/9.