Angle Terminology with Equations

Question

∠A and ∠B are vertical angles. If ∠A=(x+12)∘ and ∠B=(6x−8)∘, then find the measure of∠B.

what am I supposed to do when there are 2 xs I know they are equal to each other but even than I still cant figure out how to simplify it I'm doing this in my 7th grade advanced match class

Answer 1

So since vertical angles are equal you can set their respective algebraic expressions equal to each other.

x+12=6x - 8

Now solve for x. If what appears next is confusing, post a comment to this answer.

x - 6x = -8 - 12

-5x = -20

x=4.

If x = 4, then x+12 = 4+12 = 16.

And also, 6x-8 = 6(4)-8 = 24-8 = 16.

So each vertical angle has a measure of 16 degrees.