GEOMETRY HELP WILL MARK BRAINLIEST

x = 5 and z = 108

Step-by-step explanation:

We have two intersection lines and since z and 108 lie opposite each other, they are called vertical angles. By definition, vertical angles are congruent to each other, so that means z = 108.

Now, notice that z and 6x + 42 lie on the same line. A line has a measure of 180 degrees, which means that these two will add up to 180 (they are supplementary angles). Then we can write:

z + (6x + 42) = 180

We already know that z = 108, so plug that in and solve for x:

108 + (6x + 42) = 180

6x + 150 = 180

6x = 30

x = 5

Thus, x = 5 and z = 108.

z=108

x=5

Step-by-step explanation:

First, let's find z.

z is opposite from an angle that measures 108 degrees. Since they are opposite, they are vertical angles. This means that they are congruent or equal.

z=108

Next, let's find x.

108 and 6x+42 are on a straight line, which means they are supplementary, and add to 180 degrees.

6x+42+108=180

Combine like terms by adding 42 and 108

6x+150=180

Now, we have to solve for x, by getting x by itself.

First, subtract 150 from both sides, because 150 is being added to 6x.

6x+150-150=180-150

6x=180-150

6x=30

Next, divide both sides by 6, because 6 and x are being multiplied.

6x/6=30/6

x=30/6

x=5

So, z=108 and x=5

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step-by-step explanation: