Worksheet: Parallel Lines and Transversals: Angle 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=2𝑥69 and 𝑤=2𝑦59. Find 𝑥 and 𝑦.

  • A𝑥=83, 𝑦=78
  • B𝑥=97, 𝑦=57
  • C𝑥=83, 𝑦=71
  • D𝑥=97, 𝑦=71
  • E𝑥=76, 𝑦=78

Q3:

What is the value of 𝑥?

Q4:

Given that 𝐵𝐹𝐶𝐸, find the value of 𝑥. Then use that 𝑚𝐶𝐺𝐻=(3𝑦+2) to find the value of 𝑦.

  • A𝑥=104, 𝑦=34
  • B𝑥=76, 𝑦=102
  • C𝑥=34, 𝑦=104
  • D𝑥=76, 𝑦=34

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.

  • A𝑑=180𝑏
  • B𝑑=90+𝑏
  • C𝑑=1802𝑏
  • D𝑑=90𝑏
  • E𝑑=𝑏

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

  • A𝑎=1802𝑏
  • B𝑎=180𝑏
  • C𝑎=90+𝑏
  • D𝑎=𝑏
  • E𝑎=90𝑏

Q13:

If 𝑚2=(3𝑥+10) and 𝑚7=(2𝑥+4), find 𝑥.

Q14:

Given that 𝐴𝐵 is parallel to 𝐸𝐶, find the values of 𝑥 and 𝑦.

  • A𝑥=83, 𝑦=43
  • B𝑥=54, 𝑦=83
  • C𝑥=54, 𝑦=43
  • D𝑥=43, 𝑦=54

Q15:

Find the value of 𝑥.

  • A127
  • B125
  • C105
  • D128

Q16:

Find the value of 𝑥.

Q17:

Find the value of 𝑥.

  • A65
  • B126
  • C54
  • D76

Q18:

Given that 𝑚𝐴𝐶𝐵=76, 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
  • C32
  • D58
  • E70

Q21:

In the figure, given that 𝑚𝐴𝐵𝐶=37.5, and 𝑚𝐵𝐴𝐶=83, 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.

  • A𝑐=1802𝑏
  • B𝑐=90+2𝑏
  • C𝑐=90+𝑏
  • D𝑐=180𝑏
  • E𝑐=90𝑏

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

  • A𝑎=90+2𝑏
  • B𝑎=90+𝑏
  • C𝑎=90𝑏
  • D𝑎=180𝑏
  • E𝑎=1802𝑏

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

  • A𝑎<𝑐
  • B𝑎=𝑐
  • C𝑎>𝑐

Q23:

Given that 𝐴𝐵𝐶𝐷 and 𝐴𝐶𝐷𝐸, find the value of 𝑥.

Q24:

Find the value of 𝑥.

Q25:

Find the values of 𝑥 and 𝑦.

  • A18, 26
  • B22, 22
  • C9, 26
  • D9, 22

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.