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Worksheet: Applications of Parallel Lines

Q1:

Find π‘₯ .

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

Q2:

In the figure, what is ?

  • A
  • B
  • C
  • D

Q3:

Answer the questions for the given figure.

Find the value of π‘₯ .

Find the value of 𝑦 .

Q4:

Find .

  • A
  • B
  • C
  • D

Q5:

In the following figure, 𝑧 = 2 π‘₯ βˆ’ 6 9 and 𝑀 = 2 𝑦 βˆ’ 5 9 . Find π‘₯ and 𝑦 .

  • A π‘₯ = 7 6 , 𝑦 = 7 8
  • B π‘₯ = 8 3 , 𝑦 = 7 8
  • C π‘₯ = 8 3 , 𝑦 = 7 1
  • D π‘₯ = 9 7 , 𝑦 = 5 7
  • E π‘₯ = 9 7 , 𝑦 = 7 1

Q6:

Find .

  • A
  • B
  • C
  • D

Q7:

Find .

  • A
  • B
  • C
  • D

Q8:

Find π‘š ∠ 𝐢 𝐡 𝐴 .

Q9:

Find π‘š ∠ 𝐸 𝐷 𝐢 .

Q10:

Given that and , find .

Q11:

Find π‘₯ .

Q12:

Answer the questions for the given figure.

Find the value of π‘₯ .

Find the value of 𝑦 .

Find the value of 𝑧 .

Q13:

Given that and , find the size of .

  • A
  • B
  • C

Q14:

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

Work out the measure of angle 𝐷 𝐸 𝐢 .

Are triangles 𝐴 𝐡 𝐢 and 𝐷 𝐸 𝐢 similar? If yes, why?

  • Ayes, by the 𝐴 𝐴 criterion
  • Byes, because angle 𝐴 𝐡 𝐸 equals angle 𝐷 𝐢 𝐸 .
  • Cno

Q15:

The figure shows three parallel lines.

Find the value of π‘₯ .

Find the value of 𝑦 .

Q16:

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

Using this expression for 𝑑 , find a fully simplified expression for π‘Ž in terms of 𝑏 .

  • A π‘Ž = 𝑏
  • B π‘Ž = 1 8 0 βˆ’ 2 𝑏
  • C π‘Ž = 9 0 βˆ’ 𝑏
  • D π‘Ž = 9 0 + 𝑏
  • E π‘Ž = 1 8 0 βˆ’ 𝑏

Q17:

Given that 𝐴 𝐡 is parallel to 𝐸 𝐢 , find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 5 4 ∘ , π‘₯ = 8 3 ∘
  • B π‘₯ = 4 3 ∘ , π‘₯ = 5 4 ∘
  • C π‘₯ = 8 3 ∘ , π‘₯ = 4 3 ∘
  • D π‘₯ = 5 4 ∘ , π‘₯ = 4 3 ∘

Q18:

Which of the following is sufficient to ensure that lines 𝐿 1 and 𝐿 2 are parallel?

  • Aif 𝐿 ∩ 𝐿 = βˆ… 1 2
  • Bif 𝐿 ∩ 𝐿 = βˆ… 1 2 , where 𝐿 1 and 𝐿 2 are NOT in the same plane
  • Cif 𝐿 1 and 𝐿 2 lie in the same plane
  • Dif 𝐿 ∩ 𝐿 = βˆ… 1 2 , where 𝐿 1 and 𝐿 2 are in the same plane

Q19:

Find the value of π‘₯ .

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

Q20:

Determine .

  • A
  • B
  • C
  • D

Q21:

Find the value of π‘₯ .

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

Q22:

Find .

  • A
  • B
  • C
  • D

Q23:

In the figure below, given that π‘š ∠ 𝐴 𝐢 𝐸 = 1 3 1 ∘ , find π‘š ∠ 𝐢 𝐸 𝐹 .

Q24:

In the figure below, given that π‘š ∠ 𝐴 𝐢 𝐸 = 9 7 ∘ , find π‘š ∠ 𝐢 𝐸 𝐹 .

Q25:

Given that βƒ–     βƒ— 𝐴 𝐡 β«½ βƒ–     βƒ— 𝐢 𝐷 and π‘š ∠ 𝐸 𝐺 𝐴 = 5 9 ∘ , find π‘š ∠ 𝐷 𝐻 𝐹 .