The m6 = (11x + 8)° and m7 = (12x – 4)° What is the measure of 4? m4 = 40° m4 = 48° m4 = 132° m4 = 140°

Initially, it's important to recognize that m6 and m7 are vertical angles. Since vertical angles are congruent, we conclude that m6 is equal to m7.

m6 = m7

Next, we can substitute the values given in the problem, replacing m6 with "11x + 10" and m7 with "12x - 4." This allows us to solve for x to determine the degree measurements of both angles.

m6 = m7

Substituting the values gives us:

11x + 8 = 12x - 4

Now, we will eliminate 11x from both sides.

11x + 8 - 11x = 12x - 4 - 11x

So we have 8 = x - 4

Adding 4 on both sides leads to:

8 + 4 = x - 4 + 4

This results in x = 12.

With the value of x found, we can calculate m6 and m7.

m6 = 11x + 8

m6 = 11(12) + 8

Thus, m6 = 132 + 8

Consequently, m6 = 140.

Now for m7:

m7 = 12x - 4

Substituting gives m7 = 12(12) - 4

So m7 = 144 - 4

Therefore, m7 also equals 140.

Next, we determine m8, knowing that m6 and m8 form a straight angle which equals 180 degrees.

m6 + m8 = 180

Replace m6 with 140:

140 + m8 = 180

Subtracting 140 from both sides gives us:

m8 = 40.

With m8 determined, we can now find m4.

Using the rules regarding parallel lines and transversals, we find:

m1 = m5

m2 = m6

m3 = m7

m4 = m8

Since m4 is equivalent to m8, we can substitute the known value of 40, leading to m4 = 40.

M< 6 is equal to m< 7 since they are vertical angles.
11x + 8 = 12x – 4
12x - 11x gives 8 + 4
x = 12
therefore
m< 6 = 11x + 8
m< 6 = 11(12) + 8
m< 6 = 132 + 8
m< 6 = 140

For m< 4, we find it by subtracting m< 6 from 180
m< 4 = 180 - 140
m< 4 = 40

result

<span>m< 4 = 40</span>