Lesson Worksheet: Vertically Opposite Angles Mathematics • 7th Grade

In this worksheet, we will practice investigating the relationship between angles in intersecting lines and finding the measure of unknown angles.

Q1:

If two angles are vertically opposite, are they equal in measure?

  • AYes
  • BNo

Q2:

Given that lines ⃖⃗𝐴𝐵 and ⃖⃗𝐶𝐷 intersect at 𝑂, find 𝑚∠𝐴𝑂𝐶.

Q3:

In the figure, lines ⃖⃗𝐴𝐵 and ⃖⃗𝐶𝐷 intersect at 𝐿. What is 𝑚∠𝐴𝐿𝐷?

Q4:

Find the value of 𝑥.

Q5:

In the given diagram, 𝑚∠𝐴𝑋𝐵=(4𝑥−8)∘ and 𝑚∠𝐶𝑋𝐷=44∘. Find the value of 𝑥.

  • A𝑥=13
  • B𝑥=34
  • C𝑥=36
  • D𝑥=9
  • E𝑥=44

Q6:

Knowing that ⃖⃗𝐴𝐵∩⃖⃗𝐶𝐷∩⃖⃗𝑂𝐸={𝑀}, 𝑚∠𝐸𝑀𝐷=61∘, 𝑚∠𝐶𝑀𝐵=67∘, and 𝑚∠𝑂𝑀𝐴=𝑥, find 𝑥.

Q7:

Two intersecting straight lines are shown. Find the values of 𝑥 and 𝑦.

  • A𝑥=13, 𝑦=93
  • B𝑥=87, 𝑦=93
  • C𝑥=13, 𝑦=87
  • D𝑥=13, 𝑦=77
  • E𝑥=13, 𝑦=90

Q8:

If ∠𝑎 and ∠𝑏 are vertical angles, where 𝑚∠𝑎=(2𝑥−10)∘ and 𝑚∠𝑏=(𝑥+7)∘, find 𝑚∠𝑎 and 𝑚∠𝑏.

  • A𝑚∠𝑎=52∘, 𝑚∠𝑏=38∘
  • B𝑚∠𝑎=112∘, 𝑚∠𝑏=68∘
  • C𝑚∠𝑎=52∘, 𝑚∠𝑏=52∘
  • D𝑚∠𝑎=38∘, 𝑚∠𝑏=38∘
  • E𝑚∠𝑎=24∘, 𝑚∠𝑏=24∘

Q9:

In the figure, 𝑚∠𝐸𝑂𝐵=(8𝑥+25)∘, 𝑚∠𝐵𝑂𝐷=(6𝑥+4)∘, 𝑚∠𝐹𝑂𝐷=(3𝑦)∘, and 𝑚∠𝐴𝑂𝐹=65∘. Find the values of 𝑥 and 𝑦.

  • A𝑥=65, 𝑦=81
  • B𝑥=8, 𝑦=12
  • C𝑥=5, 𝑦=27
  • D𝑥=10, 𝑦=2
  • E𝑥=9, 𝑦=8

Q10:

In the given diagram, 𝑚∠𝐴𝑋𝐵 = 40∘. Find 𝑚∠𝐶𝑋𝐷.

Q11:

Calculate 𝑚∠𝐶𝑀𝐹.

Q12:

What is 𝑚∠𝑅𝑀𝑆 in the following figure?

Q13:

Find the value of 𝑥.

Q14:

Find the value of 𝑥 in the given diagram.

Q15:

Lines 𝐴𝐶 and 𝐵𝐷 meet at 𝑂. Determine the value of 𝑥.

Q16:

In the figure rays 𝐴𝐸 and 𝐶𝐷 meet at 𝐵, and 𝑚∠𝐷𝐵𝐸=59∘. What is 𝑚∠𝐵𝐴𝐶?

Q17:

In the given figure, if 𝑚∠𝑋𝐵𝐸=36∘ and 𝑚∠𝑍𝐴𝑌=101∘, find 𝑚∠𝐹𝐶𝐵.

Q18:

Which of the following statements is always true of vertically opposite angles?

  • AVertically opposite angles sum to 360∘.
  • BVertically opposite angles sum to 270∘.
  • CVertically opposite angles are complementary.
  • DVertically opposite angles are equal.
  • EVertically opposite angles are supplementary.

Q19:

What is the sum of the measures of the two adjacent angles formed by a straight line and a ray?

Q20:

Which of these is the supplement of an acute angle?

  • Aright angle
  • Bacute angle
  • Creflex angle
  • Dobtuse angle

Q21:

If 𝑚∠𝐴+𝑚∠𝐵=180∘, then ∠𝐴 and ∠𝐵 are .

  • Asupplementary
  • Badjacent
  • Ccomplementary
  • Dequal in measure

Q22:

Two angles are supplementary and one of them is a144∘. What is the other?

Q23:

In the given diagram, ∠𝐴𝐵𝐶 is a right angle and 𝑚∠𝐴𝐵𝐷=63∘. Work out 𝑚∠𝐷𝐵𝐶.

Q24:

Find 𝑚∠𝐴𝑂𝐵, 𝑚∠𝐴𝑂𝐸, and 𝑚∠𝐴𝑂𝐶.

  • A𝑚∠𝐴𝑂𝐵=138∘, 𝑚∠𝐴𝑂𝐸=42∘, 𝑚∠𝐴𝑂𝐶=69∘
  • B𝑚∠𝐴𝑂𝐵=138∘, 𝑚∠𝐴𝑂𝐸=69∘, 𝑚∠𝐴𝑂𝐶=42∘
  • C𝑚∠𝐴𝑂𝐵=42∘, 𝑚∠𝐴𝑂𝐸=138∘, 𝑚∠𝐴𝑂𝐶=69∘
  • D𝑚∠𝐴𝑂𝐵=69∘, 𝑚∠𝐴𝑂𝐸=138∘, 𝑚∠𝐴𝑂𝐶=42∘

Q25:

In the given diagram, 𝐴𝐵 is a straight line. Answer the following questions.

Form an equation that will allow you to calculate 𝑥.

  • A3𝑥+10=180
  • B5𝑥+20=180
  • C2𝑥+10=180
  • D5𝑥+20=90
  • E2𝑥+10=90

Find the value of 𝑥.

  • A𝑥=85
  • B𝑥=32
  • C𝑥=40
  • D𝑥=14
  • E𝑥=56

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