Answer:
130
Step-by-step explanation:
Solving the Problem
Visualize the Problem
We can start by drawing two parallel lines and a diagonal line cutting through them, and labelling them accordingly.
Then, we can label the top right angles in each intersection (2x + 18) and (4x - 14) respectively.
Lastly, label "y" to the bottom right angle at the intersection of lines b and f.
(See attached image)
[tex]\dotfill[/tex]
Angles
Recalling our knowledge of the types of angles made by parallel lines and a transversal, we can identify that (2x + 18) and (4x - 14) are corresponding angles, thus having the same measure.
Additionally, we can identify that angles (4x - 14) and y are supplementary, or have a sum of 180 degrees.
[tex]\dotfill[/tex]
Synthesize and Solve
We can set a system of equations to find our final answer,
- (2x + 18) and (4x - 14) to be equal to each other: 2x + 18 = 4x - 14,
- set an equation that sums (4x - 14) and y to 180: (4x - 14) + y = 180.
2x + 18 = 4x - 14
18 = 4x - 2x - 14 (add 2x both sides)
18 = 2x - 14 (simplify right side)
32 = 2x (add 14 both sides)
16 = x (divide by 2)
We can plug the value of x into the second equation.
4x - 14 + y = 180
4(16) - 14 + y = 180
64 - 14 + y = 180
50 + y = 180
y = 130
