Worksheet: Directed Angles

In this worksheet, we will practice identifying and measuring directed angles and finding their equivalent angles.

Q1:

Find the first negative angle which is coterminal with 190.

Q2:

Find an angle with a positive measure and an angle with a negative measure that are coterminal with an angle of 332.

  • A 5 1 2 , 2 8
  • B 6 0 2 , 2 8
  • C 2 8 , 3 3 2
  • D 6 9 2 , 2 8
  • E 2 8 , 6 9 2

Q3:

Find one angle with positive measure and one angle with negative measure which are coterminal to an angle with measure 2𝜋3.

  • A 8 𝜋 3 , 4 𝜋 3
  • B 5 𝜋 3 , 𝜋 3
  • C 4 𝜋 3 , 4 𝜋 3
  • D 8 𝜋 3 , 4 𝜋 3
  • E 8 𝜋 3 , 4 𝜋 3

Q4:

Given the angle 273𝜋3, find the principal angle.

  • A0
  • B 𝜋 3
  • C 2 𝜋
  • D 4 𝜋 3
  • E 𝜋

Q5:

Given the angle 23𝜋5, find the principal angle.

  • A 5 𝜋 3
  • B 3 𝜋 5
  • C 7 𝜋 5
  • D 3 𝜋 5
  • E 5 𝜋 7

Q6:

Find the smallest positive equivalent of 788.

Q7:

Find the positive value of an angle coterminal with 25.

  • A 2 0 5
  • B 3 8 5
  • C 2 0 5
  • D 3 8 5
  • E 3 3 5

Q8:

Find one angle with positive measure and one angle with negative measure which are coterminal to an angle with measure 3𝜋2.

  • A 7 𝜋 2 , 𝜋 2
  • B 5 𝜋 2 , 𝜋 2
  • C 𝜋 2 , 𝜋 2
  • D 7 𝜋 2 , 𝜋 2
  • E 7 𝜋 2 , 𝜋 2

Q9:

Find the positive value of an angle coterminal with 255.

  • A 4 3 5
  • B 1 0 5
  • C 4 3 5
  • D 1 0 5
  • E 6 1 5

Q10:

Find the measure of 𝜃.

Q11:

Find the smallest negative equivalent of 300.

Q12:

Find the smallest positive equivalent of 40.

  • A 1 4 0
  • B 4 0
  • C 3 2 0
  • D 1 4 0
  • E 3 2 0

Q13:

Find the smallest negative equivalent of 961.

Q14:

Find the smallest positive equivalent of 503.

  • A 2 5 4
  • B 1 4 8
  • C 2 9 1
  • D 2 1 7
  • E 7 4

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