Complementary Supplementary Angles Worksheet | Angles worksheet ... - Free Printable

Problem: Solving Complements and Supplements

The task involves finding complementary and supplementary angles, identifying pairs of supplementary angles, and determining whether given angle measurements are complementary, supplementary, or neither. Let's solve each part step by step.

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#### Part 1: Find the complement to each angle

Definition: Two angles are complementary if their measures add up to 90°.

- a. 42°
\[
\text{Complementary angle} = 90° - 42° = 48°
\]

- b. 27°
\[
\text{Complementary angle} = 90° - 27° = 63°
\]

- c. 44°
\[
\text{Complementary angle} = 90° - 44° = 46°
\]

Answers for Part 1:
- a. 48°
- b. 63°
- c. 46°

---

#### Part 2: Find the supplement to each angle

Definition: Two angles are supplementary if their measures add up to 180°.

- d. 110°
\[
\text{Supplementary angle} = 180° - 110° = 70°
\]

- e. 125°
\[
\text{Supplementary angle} = 180° - 125° = 55°
\]

- f. 87°
\[
\text{Supplementary angle} = 180° - 87° = 93°
\]

Answers for Part 2:
- d. 70°
- e. 55°
- f. 93°

---

#### Part 3: Circle the pair of angles that are supplements

We need to identify which pairs of angles add up to 180°.

- g. 121° and 107°
\[
121° + 107° = 228° \quad (\text{Not supplementary})
\]

- h. 67° and 53°
\[
67° + 53° = 120° \quad (\text{Not supplementary})
\]

- i. 77° and 77°
\[
77° + 77° = 154° \quad (\text{Not supplementary})
\]

None of the pairs add up to 180°. Therefore, there are no supplementary pairs in this section.

Answer for Part 3: None

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#### Part 4: Tell whether each pair of angle measurements are complementary, supplementary, or neither

- h. 36° and 24°
\[
36° + 24° = 60° \quad (\text{Not 90° or 180°})
\]
Answer: Neither

- i. 147° and 33°
\[
147° + 33° = 180° \quad (\text{Supplementary})
\]
Answer: Supplementary

- j. 18° and 72°
\[
18° + 72° = 90° \quad (\text{Complementary})
\]
Answer: Complementary

- k. 51° and 39°
\[
51° + 39° = 90° \quad (\text{Complementary})
\]
Answer: Complementary

- l. 67° and 105°
\[
67° + 105° = 172° \quad (\text{Not 90° or 180°})
\]
Answer: Neither

- m. 96° and 84°
\[
96° + 84° = 180° \quad (\text{Supplementary})
\]
Answer: Supplementary

Answers for Part 4:
- h. Neither
- i. Supplementary
- j. Complementary
- k. Complementary
- l. Neither
- m. Supplementary

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Final Answers:

1. Complementary angles:
- a. 48°
- b. 63°
- c. 46°

2. Supplementary angles:
- d. 70°
- e. 55°
- f. 93°

3. Pair of supplementary angles:
- None

4. Classification of angle pairs:
- h. Neither
- i. Supplementary
- j. Complementary
- k. Complementary
- l. Neither
- m. Supplementary

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
\text{1. a. 48°, b. 63°, c. 46°} \\
\text{2. d. 70°, e. 55°, f. 93°} \\
\text{3. None} \\
\text{4. h. Neither, i. Supplementary, j. Complementary, k. Complementary, l. Neither, m. Supplementary}
\end{array}
}
\]