Please help me!! I’m having a lot of trouble on this problem!

x = 17

Step-by-step explanation:

this will be our equation to find x: 2(2x - 8) = 3x +1

why? (Corresponding Angles Postulate) If two parallel lines are cut by a transversal, then the corresponding angles are congruent. in this case, it would be 2(2x - 8) would be the same as angle 5. lines a and b are the parallel lines and line c is the transversal because it cuts through both of them! Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.this means that angle 5 and 3x + 1 are the same! The Transitive Property states that for all real numbers x ,y, and z, if x=y and y=z , then x=z .in this case, x = 2(2x - 8), y = angle 5, z = 3x +1! that means if 2(2x - 8) = angle 5, angle 5 = 3x + 1, then 2(2x - 8) = 3x +1

now let's solve the equation!

2(2x - 8) = 3x + 1

4x - 16 = 3x + 1 (because of parenthese first)

x - 16 = 1

x = 17

let's check it!

3(17) + 1 = 2(2(17) - 8)

51 + 1 = 2(34 - 8)

51 + 1 = 2(26)

51 + 1 = 52

52 = 52 hooray!

comment or message me if you have any questions :)