Answer:
x = 6
y = 119
Step-by-step explanation:
Angle Relationships
When given two parallel lines with a transversal intersecting them, the angles that they create have multiple special relationships.
In the given question, we are given three angles:
∠(7x + 16)° and ∠(y + 3)° are supplementary angles, meaning they have a sum of 180 degrees. They are neighbouring angles on the same side of the transversal.
∠(y + 3)° and ∠(9x + 4)° are also supplementary angles, as they are neighbouring angles on opposite sides of the transversal and the same side of one of the parallel lines.
Moreover, ∠(7x + 16)° and ∠(9x + 4)° are equal.
All we need is 2 equations from the above information to solve for y and x. Let's use the pair of supplementary angles:
7x + 16 + y + 3 = 180
y + 3 + 9x + 4 = 180
Combine like terms:
7x + 16 + y + 3 = 180
7x + y = 161
y + 3 + 9x + 4 = 180
y + 9x = 173
Use substitution to solve for x:
y + 9x = 173
y = 173 - 9x
7x + (173 - 9x) = 161
-2x + 173 = 161
-2x = -12
x = 6
Solve for y:
y = 173 - 9x
y = 173 - 9(6)
y = 119