Worksheet: Applications of Parallel Lines

In this worksheet, we will practice using the parallelism of lines to find a missing angle depending on its relationship with another angle.

Q1:

Answer the questions for the given figure.

Find the value of 𝑥 .

Find the value of 𝑦 .

Q2:

In the given figure, 𝐷 𝐸 and 𝐴 𝐵 are parallel.

Work out the measure of angle 𝐷 𝐸 𝐶 .

Are triangles 𝐴 𝐵 𝐶 and 𝐷 𝐸 𝐶 similar? If yes, why?

  • Ayes, by the 𝐴 𝐴 criterion
  • Byes, because angle 𝐴 𝐵 𝐸 equals angle 𝐷 𝐶 𝐸 .
  • Cno

Q3:

Find 𝑥 .

  • A 1 3 4
  • B 1 3 0
  • C 1 4 1
  • D 1 3 2

Q4:

Work out the value of 𝑥 in the figure.

Q5:

Work out the value of 𝑥 in the figure.

Q6:

Work out the value of 𝑥 in the figure.

Q7:

Work out the value of 𝑥 in the figure.

Q8:

In the figure, 𝐸 𝑁 intersects 𝐴 𝐵 and 𝐶 𝐷 at 𝑀 and 𝐹 respectively. Find 𝑚 𝐸 𝐹 𝐶 .

Q9:

In the figure, what is 𝑚 𝐷 𝐹 𝑁 ?

Q10:

Find 𝑚 𝐸 𝐶 𝐷 .

Q11:

Find 𝑚 𝐶 .

Q12:

In the figure, 𝐶 𝐷 and 𝐵 𝐸 are parallel. Find 𝑚 𝐴 𝐵 𝐸 .

Q13:

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 = 8 3 , 𝑦 = 7 1
  • D 𝑥 = 9 7 , 𝑦 = 5 7
  • E 𝑥 = 9 7 , 𝑦 = 7 1

Q14:

What is the value of 𝑥 ?

Q15:

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

Q16:

In the given figure, 𝐴 𝐵 and 𝐶 𝐷 are parallel.

Work out the measure of angle 𝐴 𝐵 𝐸 .

  • A 6 3 . 5
  • B 5 3 . 1
  • C 1 2 6 . 9
  • D 6 3 . 4
  • E 1 1 6 . 5

Work out the measure of angle 𝐶 𝐸 𝐷 .

  • A 5 3 . 1
  • B 1 1 6 . 5
  • C 1 2 6 . 9
  • D 6 3 . 5
  • E 6 3 . 4

Are triangles 𝐴 𝐵 𝐸 and 𝐷 𝐶 𝐸 similar? If yes, state the criteria.

  • ANo
  • BYes, because 𝐴 𝐵 and 𝐶 𝐷 are parallel
  • CYes, by the 𝐴 𝐴 criterion

Q17:

Answer the questions for the given figure.

Find the value of 𝑥 .

Find the value of 𝑦 .

Find the value of 𝑧 .

Q18:

The figure shows three parallel lines.

Find the value of 𝑥 .

Find the value of 𝑦 .

Q19:

In the figure below, given that 𝑚 𝐴 𝐶 𝐸 = 1 3 1 , find 𝑚 𝐶 𝐸 𝐹 .

Q20:

From the information in the figure below, find 𝑚 𝐴 𝐸 𝐶 .

  • A 2 2 3
  • B 4 9
  • C 1 3 1
  • D 1 4 1

Q21:

Find 𝑚 𝐴 𝐶 𝐷 .

Q22:

Find 𝑚 𝐷 .

Q23:

Determine 𝑚 𝐸 𝐴 𝐵 .

Q24:

Find 𝑥 .

Q25:

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

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

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

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