Worksheet: Angles: Complementary and Supplementary

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In this worksheet, we will practice identifying complementary and supplementary angles and applying these relationships to find a missing angle.

Q1:

Classify the pair of angles as complementary, supplementary, or neither.

  • Asupplementary
  • Bneither
  • Ccomplementary

Q2:

State whether the given pair of angles is supplementary, complementary, or neither.

  • Aneither supplementary nor complementary
  • Bcomplementary
  • Csupplementary

Q3:

Does every right-angled triangle contain a pair of complementary angles?

  • Ano
  • Byes

Q4:

If ∠𝐴 and ∠𝐵 are complementary, 𝑚∠𝐴=𝑚∠𝐶, and ∠𝐷 complements ∠𝐶, which of the following is equal to 𝑚∠𝐵?

  • A 𝑚 ∠ 𝐴
  • B 𝑚 ∠ 𝐶
  • C 𝑚 ∠ 𝐷

Q5:

Find the measure of the angle which supplements the angle measuring 99∘.

Q6:

Find 𝑚∠𝐷𝐵𝐶.

Q7:

Given that the two angles are supplementary, find the value of 𝑥.

  • A 1 3 6 ∘
  • B 1 3 4 ∘
  • C 9 1 ∘

Q8:

Find the value of 𝑥.

Q9:

Find the value of 𝑥.

Q10:

Classify the following pair of angles as complementary, supplementary, vertical, or neither.

  • Acomplementary
  • Bneither
  • Cvertical
  • Dsupplementary

Q11:

Classify the following pair of angles as complementary, supplementary, vertical, or neither.

  • Avertical
  • Bsupplementary
  • Ccomplementary
  • Dneither

Q12:

Given the following figure, find 𝑚∠𝐵𝑂𝐷.

  • A 7 8 ∘
  • B 3 9 ∘
  • C 1 0 2 ∘
  • D 1 2 9 ∘

Q13:

In the given diagram, 𝑥 and 𝑦 are two adjacent angles that lie on the same line. Find an equation for their sum.

  • A 𝑥 + 𝑦 = 9 0 ∘
  • B 𝑥 + 𝑦 = 1 8 0 ∘
  • C 𝑥 + 𝑦 = 2 7 0 ∘
  • D 𝑥 + 𝑦 = 1 3 5 ∘
  • E 𝑥 + 𝑦 = 3 6 0 ∘

Q14:

Given the following figure, find 𝑚∠𝐵𝑂𝐴.

Q15:

A pair of supplementary angles are in the ratio of 1∶9. What is the smaller angle?

Q16:

What is the supplementary angle to 147.21∘?

  • A 3 2 . 3 9 ∘
  • B 2 3 6 . 7 9 ∘
  • C 3 2 . 7 9 ∘
  • D 3 2 ∘

Q17:

If two angles are complementary, what is the sum of their measures?

Q18:

Given that 𝑚∠𝐴𝑂𝐵=75∘, what is 𝑚∠𝐵𝑂𝐶?

Q19:

You are told that ∠𝐻 and ∠𝐴 are vertically opposite angles. If 𝑚∠𝐻=90∘, what is 𝑚∠𝐴?

Q20:

If ∠𝐴 and ∠𝐵 are both complementary and congruent, what is 𝑚∠𝐵?

Q21:

Given that ∠𝐴 and ∠𝐵 are complementary angles, and ∠𝐵 and ∠𝐶 are supplementary angles. If 𝑚∠𝐴=51∘, what is 𝑚∠𝐶?

Q22:

If the measure of ∠𝐵𝐴𝐶=61∘, what is the measure of ∠𝐵𝐴𝐹?

Q23:

Determine the values of 𝑥 and 𝑦.

  • A 𝑥 = 6 2 , 𝑦 = 3 7
  • B 𝑥 = 8 1 , 𝑦 = 5 3
  • C 𝑥 = 2 8 , 𝑦 = 5 3
  • D 𝑥 = 2 8 , 𝑦 = 8 1

Q24:

Which of the following statements is true of complementary angles?

  • AComplementary angles sum to 270∘.
  • BComplementary angles are equal.
  • CComplementary angles sum to 90∘.
  • DComplementary angles sum to 180∘.
  • EComplementary angles sum to 360∘.

Q25:

Which of the following statements is true of supplementary angles?

  • ASupplementary angles sum to 180∘.
  • BSupplementary angles sum to 360∘.
  • CSupplementary angles are equal.
  • DSupplementary angles sum to 90∘.
  • ESupplementary angles sum to 270∘.

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