Complementary and Supplementary Angles – Practice Questions

The following multiple-choice questions test your understanding of complementary and supplementary angles. Complete solutions with clear steps are provided at the bottom of the page.

Multiple Choice Questions

Question 1

Which two angles are supplementary?

  1. \(30^\circ\) and \(60^\circ\)
  2. \(41^\circ\) and \(139^\circ\)
  3. \(45^\circ\) and \(145^\circ\)
  4. \(23^\circ\) and \(147^\circ\)

Question 2

What is the complementary angle to angle \(B = \dfrac{\pi}{3}\)?

  1. \(\dfrac{\pi}{2}\)
  2. \(\dfrac{\pi}{3}\)
  3. \(\dfrac{\pi}{4}\)
  4. \(\dfrac{\pi}{6}\)

Question 3

Which two angles are complementary?

  1. \(30^\circ\) and \(130^\circ\)
  2. \(20^\circ\) and \(160^\circ\)
  3. \(45^\circ\) and \(145^\circ\)
  4. \(1^\circ\) and \(89^\circ\)

Question 4

Which of the following angles is supplementary to angle \(C = \dfrac{2\pi}{3}\)?

  1. \(\dfrac{4\pi}{3}\)
  2. \(\dfrac{2\pi}{3}\)
  3. \(\dfrac{\pi}{3}\)
  4. \(\dfrac{3\pi}{4}\)

Question 5

Which pair of angles is complementary?

  1. \(\dfrac{3\pi}{4}\) and \(\dfrac{\pi}{4}\)
  2. \(\dfrac{5\pi}{12}\) and \(\dfrac{\pi}{12}\)
  3. \(\dfrac{\pi}{4}\) and \(\dfrac{\pi}{3}\)
  4. \(\dfrac{\pi}{16}\) and \(\dfrac{\pi}{8}\)

Question 6

Which two angles are supplementary?

  1. \(\pi\) and \(\dfrac{\pi}{2}\)
  2. \(\dfrac{\pi}{3}\) and \(\dfrac{3\pi}{2}\)
  3. \(\dfrac{\pi}{7}\) and \(\dfrac{6\pi}{7}\)
  4. \(\dfrac{\pi}{8}\) and \(\dfrac{\pi}{2}\)

Answers and Step-by-Step Solutions

  1. Correct answer: b)
    Supplementary angles add up to \(180^\circ\). \[ 41^\circ + 139^\circ = 180^\circ \]
  2. Correct answer: d)
    Complementary angles add up to \(\dfrac{\pi}{2}\). \[ \dfrac{\pi}{2} - \dfrac{\pi}{3} = \dfrac{3\pi - 2\pi}{6} = \dfrac{\pi}{6} \]
  3. Correct answer: d)
    Complementary angles add up to \(90^\circ\). \[ 1^\circ + 89^\circ = 90^\circ \]
  4. Correct answer: c)
    Supplementary angles add up to \(\pi\). \[ \pi - \dfrac{2\pi}{3} = \dfrac{3\pi - 2\pi}{3} = \dfrac{\pi}{3} \]
  5. Correct answer: b)
    Complementary angles add up to \(\dfrac{\pi}{2}\). \[ \dfrac{5\pi}{12} + \dfrac{\pi}{12} = \dfrac{6\pi}{12} = \dfrac{\pi}{2} \]
  6. Correct answer: c)
    Supplementary angles add up to \(\pi\). \[ \dfrac{\pi}{7} + \dfrac{6\pi}{7} = \dfrac{7\pi}{7} = \pi \]

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