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

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.

Abdulazeez10 Abdulazeez10 · Answer 2 · 2021-10-19T13:30:04+02:00

The measure of angle 4 is 40°. That is, m4 = 40°. The correct option is the first option m4 = 40°

From the diagram, we can observe that angles 6 and 7 are vertically opposite angles.

From one of the angle theorems, we have that vertically opposite angles are equal

That means,

measure of ∠ 6 = measure of ∠ 7

From the question,

we have that, m6 = (11x + 8)° and m7 = (12x – 4)°

Since, the measures of angles 6 and 7 are equal, then we can write that

(11x + 8)° = (12x – 4)°

Now, determine the value of x, we will solve the equation

11x + 8 = 12x – 4

First, subtract 11x from both sides

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

8 = x - 4

Now, add 4 to both sides

8 + 4 = x -4 +4

12 = x

∴ x = 12

Now, we will determine the measure of ∠6

m ∠6 = (11x + 8)°

Put x = 12

∴ m ∠6 = (11(12) + 8)°

m ∠6 = (132 + 8)°

m ∠6 = 140°

To determine the measure of ∠4, m4, we will first determine the measure of ∠8.

From the diagram,

m ∠6 + m ∠8 = 180° (Sum of angles on a straight line)

∴ 140° + m ∠8 = 180°

Then,

m ∠8 = 180° - 140°

m ∠8 = 40°

From the diagram, we can observe that angles 4 and 8 are corresponding angles.

Also, from one of the angle theorems, we have that corresponding angles are equal.

Hence, the measure of ∠ 4 equals the measure of ∠ 8.

From above, m ∠8 = 40°

∴ m ∠4 = 40°

Hence, the measure of angle 4 is 40°. That is, m4 = 40°. The correct option is the first option m4 = 40°

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