Question

Please help! Geometry practice was lines cut by a transversal. What is the value of X?

Answer 1

x = 70

Explanation:

1. First, we need to know that the angle with 45 degrees and the angle with (2x-5) degrees are same-side interior angles, meaning they add up to 180 degrees. The equation of this can be written as so:
`2x-5+45= 180`

2. (Solving)

Step 1: Combine like terms.

• 
  `(2x) +(-5+45) = 180`
• 
  `2x + 40 = 180`

Step 2: Subtract 40 from both sides.

• 
  `2x + 40 - 40 = 180 - 40`
• 
  `2x = 140`

Step 3: Divide both sides by 2.

• 
  `(2x)/(2) = (140)/(2)`
• 
  `x = 70`

Step 4: Check if solution is correct.

• 
  `2(70) - 5 + 45 = 180`
• 
  `140 - 5 + 45 = 180`
• 
  `135 + 45 = 180`
• 
  `180 = 180`

Therefore, x = 70.