Worksheet: Vertically Opposite Angles

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 𝑚𝐴𝑂𝐶.

Q3:

In the figure, lines 𝐴𝐵 and 𝐶𝐷 intersect at 𝐿. What is 𝑚𝐴𝐿𝐷?

Q4:

Find the value of 𝑥.

Q5:

In the given diagram, 𝑚𝐴𝑋𝐵=(4𝑥8) and 𝑚𝐶𝑋𝐷=44. Find the value of 𝑥.

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

Q6:

Knowing that 𝐴𝐵𝐶𝐷𝑂𝐸={𝑀}, 𝑚𝐸𝑀𝐷=61, 𝑚𝐶𝑀𝐵=67, and 𝑚𝑂𝑀𝐴=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 𝑚𝑎=(2𝑥10) and 𝑚𝑏=(𝑥+7), find 𝑚𝑎 and 𝑚𝑏.

  • A𝑚𝑎=52, 𝑚𝑏=38
  • B𝑚𝑎=112, 𝑚𝑏=68
  • C𝑚𝑎=52, 𝑚𝑏=52
  • D𝑚𝑎=38, 𝑚𝑏=38
  • E𝑚𝑎=24, 𝑚𝑏=24

Q9:

In the figure, 𝑚𝐸𝑂𝐵=(8𝑥+25), 𝑚𝐵𝑂𝐷=(6𝑥+4), 𝑚𝐹𝑂𝐷=(3𝑦), and 𝑚𝐴𝑂𝐹=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, 𝑚𝐴𝑋𝐵 = 40. Find 𝑚𝐶𝑋𝐷.

Q11:

Calculate 𝑚𝐶𝑀𝐹.

Q12:

What is 𝑚𝑅𝑀𝑆 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 𝑚𝐷𝐵𝐸=59. What is 𝑚𝐵𝐴𝐶?

Q17:

In the given figure, if 𝑚𝑋𝐵𝐸=36 and 𝑚𝑍𝐴𝑌=101, find 𝑚𝐹𝐶𝐵.

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 𝑚𝐴+𝑚𝐵=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 𝑚𝐴𝐵𝐷=63. Work out 𝑚𝐷𝐵𝐶.

Q24:

Find 𝑚𝐴𝑂𝐵, 𝑚𝐴𝑂𝐸, and 𝑚𝐴𝑂𝐶.

  • A𝑚𝐴𝑂𝐵=138, 𝑚𝐴𝑂𝐸=42, 𝑚𝐴𝑂𝐶=69
  • B𝑚𝐴𝑂𝐵=138, 𝑚𝐴𝑂𝐸=69, 𝑚𝐴𝑂𝐶=42
  • C𝑚𝐴𝑂𝐵=42, 𝑚𝐴𝑂𝐸=138, 𝑚𝐴𝑂𝐶=69
  • D𝑚𝐴𝑂𝐵=69, 𝑚𝐴𝑂𝐸=138, 𝑚𝐴𝑂𝐶=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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