Question

Determine the values of x and y.

Answer 1

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]