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Lesson: Applications of Parallel Lines

Sample Question Videos

Worksheet • 25 Questions • 5 Videos

Q1:

Find π‘₯ .

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

Q2:

In the figure, what is π‘š ∠ 𝐷 𝐹 𝑁 ?

Q3:

Answer the questions for the given figure.

Find the value of π‘₯ .

Find the value of 𝑦 .

Q4:

Find π‘š ∠ 𝐸 𝐢 𝐷 .

Q5:

In the following figure, and . Find and .

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q6:

Find π‘š ∠ 𝐴 𝐢 𝐷 .

Q7:

Find π‘š ∠ 𝐴 𝐢 𝐷 .

Q8:

Find π‘š ∠ 𝐢 𝐡 𝐴 .

Q9:

Find π‘š ∠ 𝐸 𝐷 𝐢 .

Q10:

Given that  𝐴 𝐡 β«½  𝐢 𝐷 and  𝐴 𝐡 β«½ οƒͺ 𝐸 𝐹 , find π‘š ∠ 𝐴 𝐢 𝐸 .

Q11:

Find .

  • A36
  • B134
  • C46
  • D82
  • E98

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 𝐹 𝐸 β«½ 𝐴 𝐷 and π‘š ∠ 𝐹 𝐡 𝐴 = 1 1 6 ∘ , find the measure of ∠ 𝐸 𝐹 𝐺 .

Q14:

In the given figure, and are parallel.

Work out the size of angle .

  • A
  • B
  • C
  • D
  • E

Are triangles and similar? If yes, why?

  • Ano
  • Byes, by the criterion
  • Cyes, because angle equals angle .

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 = 1 8 0 βˆ’ 𝑏
  • B 𝑑 = 𝑏
  • C 𝑑 = 9 0 + 𝑏
  • D 𝑑 = 1 8 0 βˆ’ 2 𝑏
  • E 𝑑 = 9 0 βˆ’ 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’ 𝑏
  • C π‘Ž = 9 0 + 𝑏
  • D π‘Ž = 1 8 0 βˆ’ 2 𝑏
  • E π‘Ž = 9 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‘₯ = 4 3 ∘
  • B π‘₯ = 4 3 ∘ , π‘₯ = 5 4 ∘
  • C π‘₯ = 8 3 ∘ , π‘₯ = 4 3 ∘
  • D π‘₯ = 5 4 ∘ , π‘₯ = 8 3 ∘

Q18:

Which of the following is sufficient to ensure that lines 𝐿  and 𝐿  are parallel?

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

Q19:

Find the value of π‘₯ .

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

Q20:

Determine π‘š ∠ 𝐡 𝐴 𝐢 .

Q21:

Find the value of π‘₯ .

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

Q22:

Find π‘š ∠ 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 .

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