Answer:
x = 17
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!
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