Linear Pairs of Angles Worksheets - Free Printable

Problem Analysis:

The task involves identifying linear pairs of angles in given diagrams. A linear pair is defined as two adjacent angles whose non-common sides form a straight line. The key properties of a linear pair are:
1. The angles are adjacent.
2. The sum of the measures of the angles is 180° (they are supplementary).

We will solve the problem step by step for both parts.

---

Part A: Identify all the linear pairs in each figure.

#### Figure 1:
- Diagram Description: Four angles are formed at a single point, with two intersecting lines.
- Identifying Linear Pairs:
- Angles ∠1 and ∠2 are adjacent and their non-common sides form a straight line. Hence, they form a linear pair.
- Angles ∠3 and ∠4 are adjacent and their non-common sides form a straight line. Hence, they form a linear pair.

- Linear Pairs:
- ∠1 and ∠2
- ∠3 and ∠4

#### Figure 2:
- Diagram Description: Two intersecting lines form four angles.
- Identifying Linear Pairs:
- Angles ∠1 and ∠2 are adjacent and their non-common sides form a straight line. Hence, they form a linear pair.
- Angles ∠2 and ∠3 are adjacent and their non-common sides form a straight line. Hence, they form a linear pair.
- Angles ∠3 and ∠4 are adjacent and their non-common sides form a straight line. Hence, they form a linear pair.
- Angles ∠4 and ∠1 are adjacent and their non-common sides form a straight line. Hence, they form a linear pair.

- Linear Pairs:
- ∠1 and ∠2
- ∠2 and ∠3
- ∠3 and ∠4
- ∠4 and ∠1

#### Figure 3:
- Diagram Description: Three intersecting lines form multiple angles.
- Identifying Linear Pairs:
- Angles ∠1 and ∠2 are adjacent and their non-common sides form a straight line. Hence, they form a linear pair.
- Angles ∠2 and ∠3 are adjacent and their non-common sides form a straight line. Hence, they form a linear pair.
- Angles ∠3 and ∠4 are adjacent and their non-common sides form a straight line. Hence, they form a linear pair.
- Angles ∠4 and ∠1 are adjacent and their non-common sides form a straight line. Hence, they form a linear pair.

- Linear Pairs:
- ∠1 and ∠2
- ∠2 and ∠3
- ∠3 and ∠4
- ∠4 and ∠1

#### Figure 4:
- Diagram Description: Two intersecting lines form four angles.
- Identifying Linear Pairs:
- Angles ∠1 and ∠2 are adjacent and their non-common sides form a straight line. Hence, they form a linear pair.
- Angles ∠2 and ∠3 are adjacent and their non-common sides form a straight line. Hence, they form a linear pair.
- Angles ∠3 and ∠4 are adjacent and their non-common sides form a straight line. Hence, they form a linear pair.
- Angles ∠4 and ∠1 are adjacent and their non-common sides form a straight line. Hence, they form a linear pair.

- Linear Pairs:
- ∠1 and ∠2
- ∠2 and ∠3
- ∠3 and ∠4
- ∠4 and ∠1

---

Part B: Identify the angles that make a linear pair with each specified angle.

#### Given Angles:
1. ∠AOB
2. ∠DOE
3. ∠DOC
4. ∠ACF

#### Step-by-Step Identification:
We need to identify the angles that form a linear pair with each specified angle. This means we look for angles that are adjacent to the given angle and whose non-common sides form a straight line.

1. ∠AOB:
- From the diagram, ∠AOB is adjacent to ∠BOC, and their non-common sides form a straight line.
- Therefore, the linear pair with ∠AOB is ∠BOC.

2. ∠DOE:
- From the diagram, ∠DOE is adjacent to ∠EOF, and their non-common sides form a straight line.
- Therefore, the linear pair with ∠DOE is ∠EOF.

3. ∠DOC:
- From the diagram, ∠DOC is adjacent to ∠COB, and their non-common sides form a straight line.
- Therefore, the linear pair with ∠DOC is ∠COB.

4. ∠ACF:
- From the diagram, ∠ACF is adjacent to ∠FCB, and their non-common sides form a straight line.
- Therefore, the linear pair with ∠ACF is ∠FCB.

---

Final Answers:

#### Part A:
1. Figure 1: ∠1 and ∠2, ∠3 and ∠4
2. Figure 2: ∠1 and ∠2, ∠2 and ∠3, ∠3 and ∠4, ∠4 and ∠1
3. Figure 3: ∠1 and ∠2, ∠2 and ∠3, ∠3 and ∠4, ∠4 and ∠1
4. Figure 4: ∠1 and ∠2, ∠2 and ∠3, ∠3 and ∠4, ∠4 and ∠1

#### Part B:
1. ∠AOB: ∠BOC
2. ∠DOE: ∠EOF
3. ∠DOC: ∠COB
4. ∠ACF: ∠FCB

---

Boxed Final Answer:

\[
\boxed{
\text{Part A:}
1. \text{∠1 and ∠2, ∠3 and ∠4}
2. \text{∠1 and ∠2, ∠2 and ∠3, ∠3 and ∠4, ∠4 and ∠1}
3. \text{∠1 and ∠2, ∠2 and ∠3, ∠3 and ∠4, ∠4 and ∠1}
4. \text{∠1 and ∠2, ∠2 and ∠3, ∠3 and ∠4, ∠4 and ∠1}

\text{Part B:}
1. \text{∠BOC}
2. \text{∠EOF}
3. \text{∠COB}
4. \text{∠FCB}
}
\]