Worksheet: Angles: Vertically Opposite

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In this worksheet, we will practice identifying vertically opposite angles and solving their problems.

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.

  • A36
  • B38
  • C70
  • D106

Q5:

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

  • A 𝑥 = 1 3
  • B 𝑥 = 3 4
  • C 𝑥 = 3 6
  • D 𝑥 = 9
  • E 𝑥 = 4 4

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.

  • A 𝑥 = 1 3 , 𝑦 = 9 3
  • B 𝑥 = 8 7 , 𝑦 = 9 3
  • C 𝑥 = 1 3 , 𝑦 = 8 7
  • D 𝑥 = 1 3 , 𝑦 = 7 7
  • E 𝑥 = 1 3 , 𝑦 = 9 0

Q8:

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

  • A 𝑚 ∠ 𝑎 = 5 2 ∘ , 𝑚 ∠ 𝑏 = 3 8 ∘
  • B 𝑚 ∠ 𝑎 = 1 1 2 ∘ , 𝑚 ∠ 𝑏 = 6 8 ∘
  • C 𝑚 ∠ 𝑎 = 5 2 ∘ , 𝑚 ∠ 𝑏 = 5 2 ∘
  • D 𝑚 ∠ 𝑎 = 3 8 ∘ , 𝑚 ∠ 𝑏 = 3 8 ∘
  • E 𝑚 ∠ 𝑎 = 2 4 ∘ , 𝑚 ∠ 𝑏 = 2 4 ∘

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.

  • A 𝑥 = 6 5 , 𝑦 = 8 1
  • B 𝑥 = 8 , 𝑦 = 1 2
  • C 𝑥 = 5 , 𝑦 = 2 7
  • D 𝑥 = 1 0 , 𝑦 = 2
  • E 𝑥 = 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.

  • A62
  • B31
  • C118
  • D124
  • E28

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.

  • A 𝑚 ∠ 𝐴 𝑂 𝐵 = 1 3 8 ∘ , 𝑚 ∠ 𝐴 𝑂 𝐸 = 4 2 ∘ , 𝑚 ∠ 𝐴 𝑂 𝐶 = 6 9 ∘
  • B 𝑚 ∠ 𝐴 𝑂 𝐵 = 1 3 8 ∘ , 𝑚 ∠ 𝐴 𝑂 𝐸 = 6 9 ∘ , 𝑚 ∠ 𝐴 𝑂 𝐶 = 4 2 ∘
  • C 𝑚 ∠ 𝐴 𝑂 𝐵 = 4 2 ∘ , 𝑚 ∠ 𝐴 𝑂 𝐸 = 1 3 8 ∘ , 𝑚 ∠ 𝐴 𝑂 𝐶 = 6 9 ∘
  • D 𝑚 ∠ 𝐴 𝑂 𝐵 = 6 9 ∘ , 𝑚 ∠ 𝐴 𝑂 𝐸 = 1 3 8 ∘ , 𝑚 ∠ 𝐴 𝑂 𝐶 = 4 2 ∘

Q25:

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

Form an equation that will allow you to calculate 𝑥.

  • A 3 𝑥 + 1 0 = 1 8 0
  • B 5 𝑥 + 2 0 = 1 8 0
  • C 2 𝑥 + 1 0 = 1 8 0
  • D 5 𝑥 + 2 0 = 9 0
  • E 2 𝑥 + 1 0 = 9 0

Find the value of 𝑥.

  • A 𝑥 = 8 5
  • B 𝑥 = 3 2
  • C 𝑥 = 4 0
  • D 𝑥 = 1 4
  • E 𝑥 = 5 6

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