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Worksheet: Applications of Angles Relationships

Q1:

Find .

  • A
  • B
  • C
  • D

Q2:

Find , , and .

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

Q3:

These two angles are supplementary. Write and solve an equation to find π‘₯ .

Recall that two angles are supplementary if the sum of their measures is 1 8 0 ∘ .

  • A π‘₯ + 4 0 βˆ’ 4 5 = 1 8 0 , π‘₯ = 1 8 5
  • B π‘₯ + 4 0 = 4 5 , π‘₯ = 8 5
  • C π‘₯ βˆ’ 4 0 = 9 0 , π‘₯ = 1 3 0
  • D π‘₯ + 4 0 = 1 8 0 , π‘₯ = 1 4 0
  • E π‘₯ + 4 0 = 9 0 , π‘₯ = 5 0

Q4:

What is the size of ?

  • A
  • B
  • C
  • D

Q5:

Find .

  • A
  • B
  • C
  • D

Q6:

In the given diagram, 𝐴 𝐷 is a straight line, π‘š ∠ 𝐴 𝐡 𝐢 = ( 4 π‘₯ + 1 2 ) ∘ , and π‘š ∠ 𝐷 𝐡 𝐢 = 1 2 8 ∘ .

Form an equation that will allow you to calculate π‘₯ .

  • A 4 π‘₯ + 1 2 = 1 2 8
  • B 4 π‘₯ + 1 1 6 = 1 8 0
  • C 4 π‘₯ + 1 1 6 = 1 2 8
  • D 4 π‘₯ + 1 4 0 = 1 8 0
  • E 4 π‘₯ + 1 2 = 1 8 0

Solve for π‘₯ .

  • A π‘₯ = 1 0
  • B π‘₯ = 3
  • C π‘₯ = 2 9
  • D π‘₯ = 1 6
  • E π‘₯ = 4 2

Q7:

If π‘š ∠ π‘₯ = 3 7 ∘ and π‘š ∠ 𝑦 = 5 4 ∘ , find π‘š ∠ 𝑧 .

Q8:

If ∠ 𝐸 and ∠ 𝐹 are supplementary, and the measure of ∠ 𝐸 is 2 4 ∘ more than the measure of ∠ 𝐹 , find the measure of each angle.

  • A π‘š ∠ 𝐸 = 1 5 6 ∘ , π‘š ∠ 𝐹 = 2 4 ∘
  • B π‘š ∠ 𝐸 = 5 7 ∘ , π‘š ∠ 𝐹 = 3 3 ∘
  • C π‘š ∠ 𝐸 = 2 4 ∘ , π‘š ∠ 𝐹 = 1 5 6 ∘
  • D π‘š ∠ 𝐸 = 1 0 2 ∘ , π‘š ∠ 𝐹 = 7 8 ∘
  • E π‘š ∠ 𝐸 = 7 8 ∘ , π‘š ∠ 𝐹 = 1 0 2 ∘

Q9:

βƒ–    βƒ— 𝑃 𝐿 and βƒ–     βƒ— 𝐽 𝑀 are two intersecting straight lines. Given that π‘š ∠ 𝐿 𝑁 𝑀 = ( 2 π‘₯ + 2 ) ∘ and π‘š ∠ 𝐽 𝑁 𝐿 = ( 4 π‘₯ βˆ’ 1 1 ) ∘ , find π‘š ∠ 𝐽 𝑁 𝑃 .

Q10:

Determine π‘š ∠ 6 and π‘š ∠ 7 in the given figure.

  • A π‘š ∠ 6 = 2 0 3 ∘ , π‘š ∠ 7 = 2 3 ∘
  • B π‘š ∠ 6 = 6 7 ∘ , π‘š ∠ 7 = 1 1 3 ∘
  • C π‘š ∠ 6 = 2 3 ∘ , π‘š ∠ 7 = 2 0 3 ∘
  • D π‘š ∠ 6 = 1 1 3 ∘ , π‘š ∠ 7 = 6 7 ∘
  • E π‘š ∠ 6 = 2 3 ∘ , π‘š ∠ 7 = 6 7 ∘

Q11:

Given the following figure, find .

  • A
  • B
  • C
  • D

Q12:

If ∠ π‘Ž and ∠ 𝑏 form a linear pair, where π‘š ∠ π‘Ž = ( 3 π‘₯ βˆ’ 6 ) ∘ and π‘š ∠ 𝑏 = ( 7 π‘₯ + 6 ) ∘ , determine π‘š ∠ π‘Ž and π‘š ∠ 𝑏 .

  • A π‘š ∠ π‘Ž = 6 9 ∘ , π‘š ∠ 𝑏 = 2 1 ∘
  • B π‘š ∠ π‘Ž = 2 1 ∘ , π‘š ∠ 𝑏 = 6 9 ∘
  • C π‘š ∠ π‘Ž = 5 4 ∘ , π‘š ∠ 𝑏 = 1 2 6 ∘
  • D π‘š ∠ π‘Ž = 4 8 ∘ , π‘š ∠ 𝑏 = 1 3 2 ∘
  • E π‘š ∠ π‘Ž = 1 3 2 ∘ , π‘š ∠ 𝑏 = 4 8 ∘

Q13:

Find 𝑀 and 𝑧 .

  • A 𝑀 = 1 7 . 5 , 𝑧 = 2 1 . 5
  • B 𝑀 = 1 5 , 𝑧 = 3 0
  • C 𝑀 = 2 0 , 𝑧 = 1 2 . 5
  • D 𝑀 = 1 7 . 5 , 𝑧 = 2 1 . 2 5
  • E 𝑀 = 2 2 . 5 , 𝑧 = 3 . 7 5

Q14:

The rays  𝐴 𝐡 and οƒͺ 𝐡 𝐢 are perpendicular. A point 𝐷 lies in the interior of ∠ 𝐴 𝐡 𝐢 . Given that π‘š ∠ 𝐴 𝐡 𝐷 = ( 5 π‘Ÿ + 2 0 ) ∘ and π‘š ∠ 𝐷 𝐡 𝐢 = ( 8 π‘Ÿ βˆ’ 8 ) ∘ , find π‘š ∠ 𝐴 𝐡 𝐷 and π‘š ∠ 𝐷 𝐡 𝐢 .

  • A π‘š ∠ 𝐴 𝐡 𝐷 = 2 4 ∘ , π‘š ∠ 𝐷 𝐡 𝐢 = 6 6 ∘
  • B π‘š ∠ 𝐴 𝐡 𝐷 = 8 4 ∘ , π‘š ∠ 𝐷 𝐡 𝐢 = 9 5 ∘
  • C π‘š ∠ 𝐴 𝐡 𝐷 = 5 9 ∘ , π‘š ∠ 𝐷 𝐡 𝐢 = 5 4 ∘
  • D π‘š ∠ 𝐴 𝐡 𝐷 = 5 0 ∘ , π‘š ∠ 𝐷 𝐡 𝐢 = 4 0 ∘
  • E π‘š ∠ 𝐴 𝐡 𝐷 = 9 3 ∘ , π‘š ∠ 𝐷 𝐡 𝐢 = 1 1 0 ∘

Q15:

Determine .

  • A
  • B
  • C
  • D

Q16:

Given that π‘š ∠ 𝐽 = ( 3 π‘₯ βˆ’ 1 0 ) ∘ and π‘š ∠ 𝐾 = ( 4 π‘₯ + 6 ) ∘ , find π‘š ∠ 𝐾 .

Q17:

Using the fact that the lines in the figure intersect, find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 1 8 , 𝑦 = 2 4
  • B π‘₯ = 1 7 , 𝑦 = 2 3
  • C π‘₯ = 1 8 , 𝑦 = 2 2
  • D π‘₯ = 1 0 , 𝑦 = 3 2
  • E π‘₯ = 5 0 , 𝑦 = 1 3 0

Q18:

If the measure of an angle’s supplement is 6 more than three times the measure of its complement, what is the measure of that angle?

Q19:

In the given diagram, 𝐴 𝐡 and 𝐢 𝐷 are straight lines. Answer the following questions.

Form an equation that will allow you to calculate π‘₯ .

  • A 9 π‘₯ = 2 7 0
  • B 9 π‘₯ = 1 8 0
  • C 9 π‘₯ = 1 3 9
  • D 9 π‘₯ = 9 0
  • E 9 π‘₯ = 4 1

Find the value of π‘₯ .

  • A π‘₯ = 1 0
  • B π‘₯ = 1 5
  • C π‘₯ = 3 0
  • D π‘₯ = 2 0
  • E π‘₯ = 5