Worksheet: Vertically Opposite Angles

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In this worksheet, we will practice identifying vertically opposite angles.

Q1:

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

  • Ayes
  • Bno

Q2:

Given that lines ⃖ ⃗ 𝐴 𝐵 and ⃖ ⃗ 𝐶 𝐷 intersect at 𝑂 , find 𝑚 ∠ 𝐴 𝑂 𝐶 .

Q3:

In the figure, lines ⃖ ⃗ 𝐴 𝐵 and ⃖ ⃗ 𝐶 𝐷 intersect at 𝐿 . What is 𝑚 ∠ 𝐴 𝐿 𝐷 ?

Q4:

Find the value of 𝑥 .

  • A38
  • B106
  • C36
  • D70

Q5:

In the given diagram, 𝑚 ∠ 𝐴 𝑋 𝐵 = ( 4 𝑥 − 8 ) ∘ and 𝑚 ∠ 𝐶 𝑋 𝐷 = 4 4 ∘ . Find the value of 𝑥 .

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

Q6:

Knowing that ⃖ ⃗ 𝐴 𝐵 ∩ ⃖ ⃗ 𝐶 𝐷 ∩ ⃖ ⃗ 𝑂 𝐸 = { 𝑀 } , 𝑚 ∠ 𝐸 𝑀 𝐷 = 6 1 ∘ , 𝑚 ∠ 𝐶 𝑀 𝐵 = 6 7 ∘ , and 𝑚 ∠ 𝑂 𝑀 𝐴 = 𝑥 , find 𝑥 .

Q7:

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

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

Q8:

If ∠ 𝑎 and ∠ 𝑏 are vertical angles, where 𝑚 ∠ 𝑎 = ( 2 𝑥 − 1 0 ) ∘ and 𝑚 ∠ 𝑏 = ( 𝑥 + 7 ) ∘ , find 𝑚 ∠ 𝑎 and 𝑚 ∠ 𝑏 .

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

Q9:

In the figure, 𝑚 ∠ 𝐸 𝑂 𝐵 = ( 8 𝑥 + 2 5 ) ∘ , 𝑚 ∠ 𝐵 𝑂 𝐷 = ( 6 𝑥 + 4 ) ∘ , 𝑚 ∠ 𝐹 𝑂 𝐷 = ( 3 𝑦 ) ∘ , and 𝑚 ∠ 𝐴 𝑂 𝐹 = 6 5 ∘ . Find the values of 𝑥 and 𝑦 .

  • A 𝑥 = 9 , 𝑦 = 8
  • B 𝑥 = 1 0 , 𝑦 = 2
  • C 𝑥 = 8 , 𝑦 = 1 2
  • D 𝑥 = 5 , 𝑦 = 2 7
  • E 𝑥 = 6 5 , 𝑦 = 8 1

Q10:

In the given diagram, 𝑚 ∠ 𝐴 𝑋 𝐵 = 4 0 ∘ . Find 𝑚 ∠ 𝐶 𝑋 𝐷 .

Q11:

Calculate 𝑚 ∠ 𝐶 𝑀 𝐹 .

Q12:

What is 𝑚 ∠ 𝑅 𝑀 𝑆 in the following figure?

Q13:

Find the value of 𝑥 .

Q14:

Find the value of 𝑥 in the given diagram.

  • A118
  • B28
  • C31
  • D62
  • E124

Q15:

Lines 𝐴 𝐶 and 𝐵 𝐷 meet at 𝑂 . Determine the value of 𝑥 .

Q16:

In the figure rays 𝐴 𝐸 and 𝐶 𝐷 meet at 𝐵 , and 𝑚 ∠ 𝐷 𝐵 𝐸 = 5 9 ∘ . What is 𝑚 ∠ 𝐵 𝐴 𝐶 ?

Q17:

In the given figure, if 𝑚 ∠ 𝑋 𝐵 𝐸 = 3 6 ∘ and 𝑚 ∠ 𝑍 𝐴 𝑌 = 1 0 1 ∘ , find 𝑚 ∠ 𝐹 𝐶 𝐵 .

Q18:

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

  • AVertically opposite angles are supplementary.
  • BVertically opposite angles are complementary.
  • CVertically opposite angles sum to 2 7 0 ∘ .
  • DVertically opposite angles are equal.
  • EVertically opposite angles sum to 3 6 0 ∘ .

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 = 1 8 0 ∘ , then ∠ 𝐴 and ∠ 𝐵 are .

  • A equal in measure
  • B adjacent
  • C complementary
  • D supplementary

Q22:

Two angles are supplementary and one of them is a 1 4 4 ∘ . What is the other?

Q23:

In the given diagram, ∠ 𝐴 𝐵 𝐶 is a right angle and 𝑚 ∠ 𝐴 𝐵 𝐷 = 6 3 ∘ . Work out 𝑚 ∠ 𝐷 𝐵 𝐶 .

Q24:

Find 𝑚 ∠ 𝐴 𝑂 𝐵 , 𝑚 ∠ 𝐴 𝑂 𝐸 , and 𝑚 ∠ 𝐴 𝑂 𝐶 .

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

Q25:

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

Form an equation that will allow you to calculate 𝑥 .

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

Find the value of 𝑥 .

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

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