Parallel lines e and f are cut by transversal b.

Horizontal and parallel lines e and f are cut by transversal b. At the intersection of lines b and e, the uppercase right angle is (2 x + 18) degrees. At the intersection of lines b and f, the top right angle is (4 x minus 14) degrees and the bottom right angle is y degrees.

What is the value of y?

16
50
130
164

Question

30-06-2024
Mathematics

Answered

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Parallel lines e and f are cut by transversal b.

Horizontal and parallel lines e and f are cut by transversal b. At the intersection of lines b and e, the uppercase right angle is (2 x + 18) degrees. At the intersection of lines b and f, the top right angle is (4 x minus 14) degrees and the bottom right angle is y degrees.

What is the value of y?

16
50
130
164

Sagot :

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zarahaider4211 zarahaider4211 · Answer 1 · 2024-06-30T19:48:46-04:00

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

Sagot :

Solving the Problem

Visualize the Problem

Angles

Synthesize and Solve

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