You first want to take note that m6 & m7 are vertical angles. Vertical angles are equal to each other, therefore m6 is equal to m7.
m6 = m7
It tells us what m6 and m7 are in the problem, so we can replace m6 with "11x + 10" and m7 with "12x - 4." From there, we can solve for x and find out what the angles are in degrees.
m6 = m7
Replace m6 and m7.
11x + 8 = 12x - 4
Subtract 11x from both sides.
11x + 8 - 11x = 12x - 4 - 11x
8 = x - 4
Add 4 to both sides.
8 + 4 = x - 4 + 4
12 = x
Now that we have x, we can find m6 and m7.
m6 = 11x + 8
m6 = 11(12) + 8
m6 = 132 + 8
m6 = 140
And for m7.
m7 = 12x - 4
m7 = 12(12) - 4
m7 = 144 - 4
m7 = 140
From here, we can find m8 because m8 and m6 together are a straight line. Straight lines have an angle of 180 degrees.
m6 + m8 = 180
Replace m6 with 140.
140 + m8 = 180
Subtract 140 from both sides.
140 + m8 - 140 = 180 - 140
m8 = 40
Now that we have m8, we can find m4.
Because of the properties of parallel lines and transversals, we know that
m1 = m5
m2 = m6
m3 = m7
m4 = m8
Since we know m8 = 40 and m4 = m8, we can replace m8 with 40 to get m4 = 40.
