Final answer:
In a set of parallel lines, angle 2 is equal to angle 8 because they are corresponding angles. Angle 6 is equal to angle 8 because they are alternate interior angles. By solving m2 and m6 with the information given, x is found to be 26, y is found to be 136, and their sum x+y is 162.
Step-by-step explanation:
To solve the geometry question involving parallel lines and angles, we need to understand a few concepts of geometry such as alternate interior angles, corresponding angles, and the properties of parallel lines cut by a transversal. The student provided the measures of angles related to these lines: m2 = (4x-1), m6 = (y-31), and m8 = 105. Since lines j and k are parallel, certain angle pairs are congruent. Angle 8 and angle 6 are alternate interior angles, which means that they are equal when the lines are parallel. And angle 2 would be congruent to angle 8 as well since they would be corresponding angles.
Firstly, since m8=105, we can set it equal to m6:
105 = y - 31
Adding 31 to both sides, we get:
y = 136
Similarly, we can set m2 equal to m8 because they are corresponding angles:
(4x-1) = 105
Adding 1 to both sides and then dividing by 4:
x = 26
In conclusion, to find the value of x+y, we add the x value of 26 to the y value of 136:
x+y = 26+136
x+y = 162
The correct equation to find the sum of x and y is:
x+y = (4x-1) + (y-31) when m2 = m8 = 105