Question

Can someone explain to me how to do this

Answer 1

y = 18

x = 46

measures of the angles:

8y - 102 = 42

2y + 6 = 42

3x = 138

Explanation:

So first remember the verticle angles theorem, which states that, when two lines intersect there will be four angles formed; the angles that are opposite from each other will be congruent, that is, they will have the same measure.

Using this we know that opposite angles have to be congruent:

so

(2y + 6) = (8y -102)

now there is an algebra equation that can be solved by inverse operations and simplifying

2y + 6 = 8y - 102

+102 +102

2y + 108 = 8y

-2y -2y

108 = 6y

/6 /6

18 = y

Also, remember that two adjacent angles that form a line will add up to 180,

so

3x + (2y + 6) = 180

*note: I could have also used (8y - 102) but I choose to use (2y + 6)

so now substitute in the value of y that was found

y = 18

3x + (2 * 18 + 6) = 180

simplify

3x + ( 36 + 6) = 180

3x + 42 = 180

now use inverse operations

3x + 42 = 180

-42 -42

3x = 138

/3 /3

x = 46

Answer 2

x=45

Explanation:

We know that 2y+6 and 8y-102 are vertical angles to each other. This means that 2y+6=8y-102.
`6y=108`, which means that y=18.
`2\cdot(18)+6=36+6=42`. Since one line is a straight angle, it is 180 degrees we can do
`3x=180-45=135`, so x=45.