Worksheet: Applications of Angles Relationships

In this worksheet, we will practice finding a missing angle measure using the relations between complementary, supplementary, or vertically opposite angles.

Q1:

What is the measure of ∠ 𝑍 𝐹 π‘Œ ?

Q2:

Find π‘š ∠ 𝐢 .

Q3:

Find π‘š ∠ 𝐴 𝑂 𝐡 , π‘š ∠ 𝐴 𝑂 𝐸 , and π‘š ∠ 𝐷 𝑂 𝐸 .

  • A π‘š ∠ 𝐴 𝑂 𝐡 = 1 4 2 ∘ , π‘š ∠ 𝐴 𝑂 𝐸 = 3 8 ∘ , π‘š ∠ 𝐷 𝑂 𝐸 = 1 4 2 ∘
  • B π‘š ∠ 𝐴 𝑂 𝐡 = 3 8 ∘ , π‘š ∠ 𝐴 𝑂 𝐸 = 3 8 ∘ , π‘š ∠ 𝐷 𝑂 𝐸 = 1 4 2 ∘
  • C π‘š ∠ 𝐴 𝑂 𝐡 = 1 4 2 ∘ , π‘š ∠ 𝐴 𝑂 𝐸 = 3 8 ∘ , π‘š ∠ 𝐷 𝑂 𝐸 = 3 8 ∘
  • D π‘š ∠ 𝐴 𝑂 𝐡 = 3 8 ∘ , π‘š ∠ 𝐴 𝑂 𝐸 = 1 4 2 ∘ , π‘š ∠ 𝐷 𝑂 𝐸 = 3 8 ∘

Q4:

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 ∘

Q5:

Find π‘š ∠ 𝑋 𝐴 𝐢 .

Q6:

Determine π‘š ∠ 𝐷 𝑋 𝐢 .

Q7:

If and , find .

  • A
  • B
  • C
  • D
  • E

Q8:

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

  • A
  • B
  • C
  • D
  • E

Q9:

Given the following figure, find π‘š ∠ 𝐡 𝑂 𝐴 .

Q10:

and are two intersecting straight lines. Given that and , find .

  • A
  • B
  • C
  • D
  • E

Q11:

If and form a linear pair, where and , determine and .

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

Q12:

These two angles are supplementary. Write and solve an equation to find .

Recall that two angles are supplementary if the sum of their sizes is .

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

Q13:

The rays and are perpendicular. A point lies in the interior of . Given that and , find and .

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

Q14:

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

Q15:

Given that and , find .

  • A
  • B
  • C
  • D
  • E

Q16:

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

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 and are supplementary, and the size of is more than the size of , find the size of each angle.

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

Q19:

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

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