Question

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

Answer 1

M< 6 = m< 7 (vertical angles)
11x + 8 = 12x – 4
12x - 11x = 8 + 4
 x = 12
so
m< 6 = 11x + 8 
m< 6 = 11(12) + 8
m< 6 = 132 + 8
m< 6 = 140

m<4 = 180 - m<6
m<4 = 180 - 140
m<4 = 40

answer

m<4 = 40

Answer 2

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.