Worksheet: Parallel Lines and Transversals: Angle Relationships

In this worksheet, we will practice naming and identifying angle pairs formed by parallel lines and transversals and recognizing their relationships to find a missing angle.

Q1:

In the given figure, 𝐷𝐸 and 𝐴𝐵 are parallel.

Work out the measure of angle 𝐷𝐸𝐶.

Are triangles 𝐴𝐵𝐶 and 𝐷𝐸𝐶 similar? If yes, why?

  • Ayes, because angle 𝐴𝐵𝐸 equals angle 𝐷𝐶𝐸.
  • Byes, by the 𝐴𝐴 criterion
  • Cno

Q2:

Find 𝑥.

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

Q3:

In the figure, 𝐸𝑁 intersects 𝐴𝐵 and 𝐶𝐷 at 𝑀 and 𝐹 respectively. Find 𝑚𝐸𝐹𝐶.

Q4:

In the figure, what is 𝑚𝐷𝐹𝑁?

Q5:

Find 𝑚𝐸𝐶𝐷.

Q6:

Find 𝑚𝐶.

Q7:

In the figure, 𝐶𝐷 and 𝐵𝐸 are parallel. Find 𝑚𝐴𝐵𝐸.

Q8:

In the given figure, 𝐴𝐵 and 𝐶𝐷 are parallel.

Work out the measure of angle 𝐴𝐵𝐸.

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

Work out the measure of angle 𝐶𝐸𝐷.

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

Are triangles 𝐴𝐵𝐸 and 𝐷𝐶𝐸 similar? If yes, state the criteria.

  • AYes, by the 𝐴𝐴 criterion
  • BYes, because 𝐴𝐵 and 𝐶𝐷 are parallel
  • CNo

Q9:

In the figure below, given that 𝑚𝐴𝐶𝐸=131, find 𝑚𝐶𝐸𝐹.

Q10:

From the information in the figure below, find 𝑚𝐴𝐸𝐶.

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

Q11:

Find 𝑚𝐴𝐶𝐷.

Q12:

Find 𝑚𝐷.

Q13:

Determine 𝑚𝐸𝐴𝐵.

Q14:

Given that 𝐴𝐵𝐶𝐷, find 𝑚𝐸𝐹𝐵.

Q15:

Find 𝑚𝐴𝐶𝐷.

Q16:

Find 𝑚𝐶𝐵𝐴.

Q17:

Find 𝑚𝐷.

Q18:

In the figure 𝐴𝐵𝐶𝐷. Find 𝑚𝐸𝐹𝐵.

Q19:

Find 𝑚𝐸𝐷𝐶.

Q20:

Given that 𝐴𝐵𝐶𝐷 and 𝐴𝐵𝐸𝐹, find 𝑚𝐴𝐶𝐸.

Q21:

Given that 𝐶𝐵=𝐴𝐵, 𝐴𝐶𝐵𝐸, 𝑚𝐴𝐵𝐶=98, and the point 𝐷 lies on the ray 𝐴𝐵, determine the measure of 𝐸𝐵𝐷.

Q22:

Given that 𝐹𝐸𝐴𝐷 and 𝑚𝐹𝐵𝐴=116, find the measure of 𝐸𝐹𝐺.

Q23:

Given that 𝐴𝐷 is parallel to 𝐵𝐶 and the points 𝐴, 𝐶, and 𝐸 are collinear, find the measure of all the angles of 𝐴𝐵𝐶.

  • A 𝑚 𝐴 = 4 4 , 𝑚 𝐵 = 4 6 , 𝑚 𝐶 = 4 6
  • B 𝑚 𝐴 = 4 4 , 𝑚 𝐵 = 4 3 , 𝑚 𝐶 = 4 3
  • C 𝑚 𝐴 = 9 1 , 𝑚 𝐵 = 4 3 , 𝑚 𝐶 = 4 6
  • D 𝑚 𝐴 = 9 1 , 𝑚 𝐵 = 4 6 , 𝑚 𝐶 = 4 3

Q24:

Find 𝑚𝐹𝐺𝐸.

Q25:

In the figure, 𝐴𝐷 is a median of triangle 𝐴𝐵𝐶. Use the information given to determine 𝑚𝐹𝐷𝐶.

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