Pairs of Angles Worksheets - Free Printable

Problem Analysis:

The task involves two parts related to adjacent angles:

1. Part (a): Identify which figures show adjacent angles.
2. Part (b): Identify two pairs of adjacent angles in each diagram.

#### Definitions:
- Adjacent Angles: Two angles are adjacent if they share a common vertex and a common side, but do not overlap. The non-common sides of the angles form a straight line or are part of the same geometric figure.

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Solution:

#### Part (a): Identify which figures show adjacent angles.
We need to analyze each figure to determine if it contains adjacent angles.

1. Figure 1:
- The two angles share a common vertex and a common side.
- The non-common sides form a straight line.
- Conclusion: This is a pair of adjacent angles.

2. Figure 2:
- The two angles share a common vertex and a common side.
- The non-common sides form a straight line.
- Conclusion: This is a pair of adjacent angles.

3. Figure 3:
- The two angles share a common vertex and a common side.
- The non-common sides form a straight line.
- Conclusion: This is a pair of adjacent angles.

4. Figure 4:
- The two angles do not share a common side.
- They are separate and do not form adjacent angles.
- Conclusion: This is not a pair of adjacent angles.

5. Figure 5:
- The two angles share a common vertex and a common side.
- The non-common sides form a straight line.
- Conclusion: This is a pair of adjacent angles.

6. Figure 6:
- The two angles share a common vertex and a common side.
- The non-common sides form a straight line.
- Conclusion: This is a pair of adjacent angles.

#### Final Answer for Part (a):
The figures that show adjacent angles are: Figures 1, 2, 3, 5, and 6.

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#### Part (b): Identify two pairs of adjacent angles in each diagram.
We now analyze each diagram to identify two pairs of adjacent angles.

1. Diagram 1:
- Pair 1: The angle formed by the horizontal line and the diagonal line on the left.
- Pair 2: The angle formed by the horizontal line and the diagonal line on the right.
- Both pairs share a common vertex and a common side with their respective adjacent angles.

2. Diagram 2:
- Pair 1: The angle formed by the vertical line and the diagonal line on the top.
- Pair 2: The angle formed by the vertical line and the diagonal line on the bottom.
- Both pairs share a common vertex and a common side with their respective adjacent angles.

3. Diagram 3:
- Pair 1: The angle formed by the horizontal line and the diagonal line on the left.
- Pair 2: The angle formed by the horizontal line and the diagonal line on the right.
- Both pairs share a common vertex and a common side with their respective adjacent angles.

#### Final Answer for Part (b):
- Diagram 1: Two pairs of adjacent angles are identified as described above.
- Diagram 2: Two pairs of adjacent angles are identified as described above.
- Diagram 3: Two pairs of adjacent angles are identified as described above.

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Final Boxed Answers:

- Part (a): Figures 1, 2, 3, 5, and 6 show adjacent angles.
- Part (b): Two pairs of adjacent angles are identified in each diagram as explained.

$$
\boxed{\text{Figures 1, 2, 3, 5, and 6; Pairs of adjacent angles as described}}
$$