Worksheet: Parallel Lines and Transversals: Angles Applications

In this worksheet, we will practice using angle relationships formed by parallel lines and transversals to solve problems involving algebraic expressions and equations.

Q1:

Answer the questions for the given figure.

Find the value of 𝑥 .

Find the value of 𝑦 .

Q2:

In the following figure, 𝑧 = 2 𝑥 6 9 and 𝑤 = 2 𝑦 5 9 . Find 𝑥 and 𝑦 .

  • A 𝑥 = 7 6 , 𝑦 = 7 8
  • B 𝑥 = 8 3 , 𝑦 = 7 8
  • C 𝑥 = 9 7 , 𝑦 = 5 7
  • D 𝑥 = 9 7 , 𝑦 = 7 1
  • E 𝑥 = 8 3 , 𝑦 = 7 1

Q3:

What is the value of 𝑥 ?

Q4:

Given that 𝐵 𝐹 𝐶 𝐸 , find the value of 𝑥 . Then use that 𝑚 𝐶 𝐺 𝐻 = ( 3 𝑦 + 2 ) to find the value of 𝑦 .

  • A 𝑥 = 3 4 , 𝑦 = 1 0 4
  • B 𝑥 = 7 6 , 𝑦 = 3 4
  • C 𝑥 = 1 0 4 , 𝑦 = 3 4
  • D 𝑥 = 7 6 , 𝑦 = 1 0 2

Q5:

Answer the questions for the given figure.

Find the value of 𝑥 .

Find the value of 𝑦 .

Find the value of 𝑧 .

Q6:

The figure shows three parallel lines.

Find the value of 𝑥 .

Find the value of 𝑦 .

Q7:

Work out the value of 𝑥 in the figure.

Q8:

Work out the value of 𝑥 in the figure.

Q9:

Work out the value of 𝑥 in the figure.

Q10:

Work out the value of 𝑥 in the figure.

Q11:

Find 𝑥 .

Q12:

The given figure shows a pair of parallel lines and two transversals, one of which crosses at right angles.

Write an expression for 𝑑 in terms of 𝑏 .

  • A 𝑑 = 1 8 0 2 𝑏
  • B 𝑑 = 1 8 0 𝑏
  • C 𝑑 = 𝑏
  • D 𝑑 = 9 0 𝑏
  • E 𝑑 = 9 0 + 𝑏

Using this expression for 𝑑 , find a fully simplified expression for 𝑎 in terms of 𝑏 .

  • A 𝑎 = 1 8 0 2 𝑏
  • B 𝑎 = 9 0 𝑏
  • C 𝑎 = 1 8 0 𝑏
  • D 𝑎 = 𝑏
  • E 𝑎 = 9 0 + 𝑏

Q13:

If 𝑚 2 = ( 3 𝑥 + 1 0 ) and 𝑚 7 = ( 2 𝑥 + 4 ) , find 𝑥 .

Q14:

Given that 𝐴 𝐵 is parallel to 𝐸 𝐶 , find the values of 𝑥 and 𝑦 .

  • A 𝑥 = 5 4 , 𝑦 = 4 3
  • B 𝑥 = 4 3 , 𝑦 = 5 4
  • C 𝑥 = 5 4 , 𝑦 = 8 3
  • D 𝑥 = 8 3 , 𝑦 = 4 3

Q15:

Find the value of 𝑥 .

  • A 1 2 8
  • B 1 0 5
  • C 1 2 7
  • D 1 2 5

Q16:

Find the value of 𝑥 .

  • A 1 2 5
  • B 1 1 2
  • C 1 0 4
  • D 1 4 4

Q17:

Find the value of 𝑥 .

  • A 6 5
  • B 1 2 6
  • C 7 6
  • D 5 4

Q18:

Given that 𝑚 𝐴 𝐶 𝐵 = 7 6 , determine the measure of 𝑥 .

Q19:

Answer the questions for the given figure.

Find the value of 𝑥 .

Find the value of 𝑦 .

Find the value of 𝑧 .

Q20:

Answer the questions for the given figure.

Find the value of 𝑥 .

Find the value of 𝑦 .

Find the value of 𝑧 .

  • A78
  • B12
  • C58
  • D70
  • E32

Q21:

In the figure, given that 𝑚 𝐴 𝐵 𝐶 = 3 7 . 5 , and 𝑚 𝐵 𝐴 𝐶 = 8 3 , determine the value of 𝑥 .

Q22:

The given figure shows two lines intersecting a pair of parallel lines, one of which intersects the lines at right angles.

Find an expression for 𝑐 in terms of 𝑏 .

  • A 𝑐 = 9 0 + 𝑏
  • B 𝑐 = 9 0 + 2 𝑏
  • C 𝑐 = 1 8 0 𝑏
  • D 𝑐 = 1 8 0 2 𝑏
  • E 𝑐 = 9 0 𝑏

Using what you know about the sum of angles in a quadrilateral, find an expression for 𝑎 in terms of 𝑏 .

  • A 𝑎 = 1 8 0 2 𝑏
  • B 𝑎 = 9 0 𝑏
  • C 𝑎 = 9 0 + 𝑏
  • D 𝑎 = 9 0 + 2 𝑏
  • E 𝑎 = 1 8 0 𝑏

Hence, what is true of the angular measures 𝑎 and 𝑐 ?

  • A 𝑎 < 𝑐
  • B 𝑎 = 𝑐
  • C 𝑎 > 𝑐

Q23:

Given that 𝐴 𝐵 𝐶 𝐷 and 𝐴 𝐶 𝐷 𝐸 , find the value of 𝑥 .

  • A 6 0
  • B 6 8
  • C 5 9
  • D 1 2 0

Q24:

Find the value of 𝑥 .

Q25:

Find the values of 𝑥 and 𝑦 .

  • A9, 22
  • B18, 26
  • C9, 26
  • D22, 22

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