Answer:
x = 100
y = 44
Explanation:
The interior angles of a quadrilateral add up to 360 degrees, so we know that when all four angles are added together, they need to equal 360.
121 + 111 + x - 31 + 2y - 29 = 360
Additionally, the angles opposite each other equals 180 degrees. This means D + F = 180 degrees, and E + G = 180 degrees.
111 + (x - 31) = 180
Subtract 111 from both sides.
x - 31 = 69
Add 31 to each side
x = 100
Plug in the value for x to check the answer
111 + (100 - 31) = 180
Then, for y, we have the same set up
121 + (2y - 29) = 180
Subtract 121 from both sides
2y - 29 = 59
Add 29 to each side
2y = 88
Divide each side by 2
y = 44
Plug in the value for y to check the answer
121 + (2*44 - 29) = 180
This means that angle F equals 59 degrees and angle G equals 69 degrees.
x = 100
y = 44