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.

  • A512, 28
  • B602, 28
  • C28, 332
  • D692, 28
  • E28, 692

Q3:

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

  • A8𝜋3, 4𝜋3
  • B5𝜋3, 𝜋3
  • C4𝜋3, 4𝜋3
  • D8𝜋3, 4𝜋3
  • E8𝜋3, 4𝜋3

Q4:

Given the angle 273𝜋3, find the principal angle.

  • A0
  • B𝜋3
  • C2𝜋
  • D4𝜋3
  • E𝜋

Q5:

Given the angle 23𝜋5, find the principal angle.

  • A5𝜋3
  • B3𝜋5
  • C7𝜋5
  • D3𝜋5
  • E5𝜋7

Q6:

Find the smallest positive equivalent of 788.

Q7:

Find the positive value of an angle coterminal with 25.

Q8:

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

  • A7𝜋2, 𝜋2
  • B5𝜋2, 𝜋2
  • C𝜋2, 𝜋2
  • D7𝜋2, 𝜋2
  • E7𝜋2, 𝜋2

Q9:

Find the positive value of an angle coterminal with 255.

Q10:

Find the measure of 𝜃.

Q11:

Find the smallest negative equivalent of 300.

Q12:

Find the smallest positive equivalent of 40.

Q13:

Find the smallest negative equivalent of 961.

Q14:

Find the smallest positive equivalent of 503.

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