Based on the diagram shown below, the value of x - y is equal to 3y + 10x.
Since M is the midpoint of line segment AB, we can logically deduce the following:
Line segment AM = Line segment MB
25x + y = 5x - y
25x - 5x = -y - y
20x = -2y
10x = -y
y = -10x ...............equation 1.
By applying the vertical angles theorem to the lines, we have;
m∠AMC ≅ m∠CMB
11x - 11y = 9x - 5y
11x - 9x = 11y - 5y
2x = 6y
x = 3y ...............equation 2.
Next, we would determine the value of x - y by using the substitution method;
x - y
3y - (-10x)
3y + 10x
Complete Question:
Solve for the value of x - y. Given the following information. AM=25x + y, MB= 5x- y, m∠AMC = 11x -11y, m∠CMB =9x-5y.