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Brilliant_brown [7]
2 years ago
5

Determine the values of x and y.

Mathematics
1 answer:
mart [117]2 years ago
5 0

Answer: x = 23, y = 40

Step-by-step 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]
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