Worksheet: Angles: Vertically Opposite

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 𝑚𝐴𝑂𝐶.

Q3:

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

Q4:

Find the value of 𝑥.

  • A36
  • B38
  • C70
  • D106

Q5:

In the given diagram, 𝑚𝐴𝑋𝐵=(4𝑥8) and 𝑚𝐶𝑋𝐷=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 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.

  • 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 𝑚𝑎=(2𝑥10) and 𝑚𝑏=(𝑥+7), find 𝑚𝑎 and 𝑚𝑏.

  • 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, 𝑚𝐸𝑂𝐵=(8𝑥+25), 𝑚𝐵𝑂𝐷=(6𝑥+4), 𝑚𝐹𝑂𝐷=(3𝑦), and 𝑚𝐴𝑂𝐹=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, 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.

  • 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 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.

  • 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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