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Worksheet: Vertically Opposite Angles

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

Q1:

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

  • Ayes
  • Bno

Q2:

Given that lines and intersect at , find .

  • A
  • B
  • C
  • D

Q3:

Given that lines and intersect at , find .

  • A
  • B
  • C
  • D

Q4:

In the figure, lines and intersect at . What is ?

  • A
  • B
  • C
  • D

Q5:

Find the value of .

  • A38
  • B106
  • C36
  • D70

Q6:

Find the value of .

  • A34
  • B114
  • C32
  • D82

Q7:

In the given diagram, π‘š ∠ 𝐴 𝑋 𝐡 = ( 4 π‘₯ βˆ’ 8 ) ∘ and π‘š ∠ 𝐢 𝑋 𝐷 = 4 4 ∘ . Find the value of π‘₯ .

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

Q8:

Knowing that , , , and , find .

  • A
  • B
  • C
  • D

Q9:

Two intersecting straight lines are shown. Find the values of π‘₯ and 𝑦 .

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

Q10:

If ∠ π‘Ž and ∠ 𝑏 are vertical angles, where π‘š ∠ π‘Ž = ( 2 π‘₯ βˆ’ 1 0 ) ∘ and π‘š ∠ 𝑏 = ( π‘₯ + 7 ) ∘ , find π‘š ∠ π‘Ž and π‘š ∠ 𝑏 .

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

Q11:

In the figure, π‘š ∠ 𝐸 𝑂 𝐡 = ( 8 π‘₯ + 2 5 ) ∘ , π‘š ∠ 𝐡 𝑂 𝐷 = ( 6 π‘₯ + 4 ) ∘ , π‘š ∠ 𝐹 𝑂 𝐷 = ( 3 𝑦 ) ∘ , and π‘š ∠ 𝐴 𝑂 𝐹 = 6 5 ∘ . Find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 9 , 𝑦 = 8
  • B π‘₯ = 1 0 , 𝑦 = 2
  • C π‘₯ = 8 , 𝑦 = 1 2
  • D π‘₯ = 5 , 𝑦 = 2 7
  • E π‘₯ = 6 5 , 𝑦 = 8 1

Q12:

In the given diagram, π‘š ∠ 𝐴 𝑋 𝐡 = 4 0 ∘ . Find π‘š ∠ 𝐢 𝑋 𝐷 .

Q13:

Calculate .

  • A
  • B
  • C
  • D
  • E

Q14:

What is π‘š ∠ 𝑅 𝑀 𝑆 in the following figure?

Q15:

Find the value of π‘₯ .

Q16:

Find the value of π‘₯ in the given diagram.

  • A118
  • B28
  • C31
  • D62
  • E124

Q17:

Lines and meet at . Determine the value of .

  • A
  • B
  • C
  • D

Q18:

In the figure rays and meet at , and . What is ?

  • A
  • B
  • C
  • D

Q19:

In the given figure, if π‘š ∠ 𝑋 𝐡 𝐸 = 3 6 ∘ and π‘š ∠ 𝑍 𝐴 π‘Œ = 1 0 1 ∘ , find π‘š ∠ 𝐹 𝐢 𝐡 .

  • A 7 9 ∘
  • B 1 4 4 ∘
  • C 3 6 ∘
  • D 1 3 7 ∘

Q20:

Which of the following statements is true of complementary angles?

  • AComplementary angles are equal.
  • BComplementary angles sum to 1 8 0 ∘ .
  • CComplementary angles sum to 2 7 0 ∘ .
  • DComplementary angles sum to 9 0 ∘ .
  • EComplementary angles sum to 3 6 0 ∘ .

Q21:

Which of the following statements is true of supplementary angles?

  • ASupplementary angles are equal.
  • BSupplementary angles sum to 9 0 ∘ .
  • CSupplementary angles sum to 2 7 0 ∘ .
  • DSupplementary angles sum to 1 8 0 ∘ .
  • ESupplementary angles sum to 3 6 0 ∘ .

Q22:

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 ∘ .

Q23:

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

  • A
  • B
  • C
  • D

Q24:

Which of these is the supplement of an acute angle?

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

Q25:

If π‘š ∠ 𝐴 + π‘š ∠ 𝐡 = 1 8 0 ∘ , then ∠ 𝐴 and ∠ 𝐡 are .

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

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