- The problem involves finding the value of `x` for different angle pairs formed by parallel lines and a transversal.
- For problem 1: The angles `(x + 26)°` and `(2x - 20)°` are alternate interior angles, so they are equal. Setting them equal gives `x + 26 = 2x - 20`. Solving for `x` yields `x = 46`.
- For problem 2: The angle `(2x - 80)°` is adjacent to a right angle (90°), forming a linear pair. So, `(2x - 80) + 90 = 180`. Solving for `x` yields `x = 85`.
- For problem 3: The angles `(x + 20)°` and `(7x - 1)°` are corresponding angles, so they are equal. Setting them equal gives `x + 20 = 7x - 1`. Solving for `x` yields `x = 3.5`.
- For problem 4: The angles `(x + 96)°` and `(3x - 9)°` are same-side interior angles, so they are supplementary. Setting their sum to 180 gives `(x + 96) + (3x - 9) = 180`. Solving for `x` yields `x = 23.25`.
- For problem 5: The angles `(4x + 25)°` and `(6x + 8)°` are vertical angles, so they are equal. Setting them equal gives `4x + 25 = 6x + 8`. Solving for `x` yields `x = 8.5`.
- For problem 6: The angles `(7x - 1)°` and `(6x + 8)°` are adjacent angles forming a linear pair. So, `(7x - 1) + (6x + 8) = 180`. Solving for `x` yields `x = 13.3077` (approximately).
- For problem 7: The angle `(3x - 15)°` is an alternate exterior angle to a given angle, which must be equal. Assuming it equals a known angle or using the diagram's context, if it's equal to another angle not shown numerically, this might need more context. However, if we assume it's part of a linear pair with a known angle, further information is needed. Without additional context, this problem cannot be solved definitively from the given text alone.
- For problem 8: The angles `147°` and `(2x - 23)°` are vertical angles, so they are equal. Setting them equal gives `147 = 2x - 23`. Solving for `x` yields `x = 85`.
- For problem 9: The angle `(14x - 1)°` is an alternate interior angle to a given angle, which must be equal. Assuming it equals a known angle or using the diagram's context, if it's equal to another angle not shown numerically, this might need more context. However, if we assume it's part of a linear pair with a known angle, further information is needed. Without additional context, this problem cannot be solved definitively from the given text alone.
Parent Tip: Review the logic above to help your child master the concept of angle pairs worksheet.
