Answer: x = 23, y = 40
Explanation:
By the same-side interior angles theorem, y+30 and 110 are supplementary.
- 110 + y + 30 = 180 [supplementary angles add to 180 degrees]
- y + 140 = 180 [combine like terms]
- y = 40 [subtract 140 from both sides]
We know that the 3x + 1 angle and y + 30 are also congruent, so:
- 3x + 1 = y + 30 [congruent angles have equal measure]
- 3x + 1 = 40 + 30 [substitute y = 40]
- 3x + 1 = 70 [combine like terms]
- 3x = 69 [subtract 1 from both sides]
- x = 23 [divide both sides by 3]