Geometry worksheet focusing on angle relationships including adjacent, vertical, complementary, supplementary, and linear pairs.

Problem Analysis:

The task involves identifying pairs of angles in the given diagrams as adjacent, vertical, complementary, supplementary, or linear pair. Additionally, there are questions at the end that require identifying specific types of angle pairs in a provided figure.

#### Definitions of Angle Types:
1. Adjacent Angles: Two angles that share a common vertex and a common side but do not overlap.
2. Vertical Angles: Angles opposite each other when two lines intersect. They are always congruent.
3. Complementary Angles: Two angles whose measures add up to 90°.
4. Supplementary Angles: Two angles whose measures add up to 180°.
5. Linear Pair: Two adjacent angles that form a straight line (their measures add up to 180°).

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Step-by-Step Solution:

#### Part 1: Identifying Angle Pairs in Diagrams 1–9

We will analyze each diagram and identify the type of angle pair(s) present.

##### Diagram 1:
- There are two angles formed by a transversal crossing two parallel lines.
- The angles are adjacent because they share a common vertex and a common side.
- Answer: Adjacent angles.

##### Diagram 2:
- Two lines intersect, forming four angles.
- The angles directly opposite each other are vertical angles.
- Answer: Vertical angles.

##### Diagram 3:
- Two angles are shown, and their measures add up to 180° (one is labeled as 120°, and the other is implied to be 60°).
- These angles are supplementary.
- Answer: Supplementary angles.

##### Diagram 4:
- Two angles are shown, and their measures add up to 90° (one is labeled as 30°, and the other is implied to be 60°).
- These angles are complementary.
- Answer: Complementary angles.

##### Diagram 5:
- Two angles are shown, and their measures add up to 180° (one is labeled as 110°, and the other is implied to be 70°).
- These angles are supplementary.
- Answer: Supplementary angles.

##### Diagram 6:
- Two angles are shown, and their measures add up to 90° (one is labeled as 45°, and the other is implied to be 45°).
- These angles are complementary.
- Answer: Complementary angles.

##### Diagram 7:
- Two angles are shown, and their measures add up to 180° (one is labeled as 130°, and the other is implied to be 50°).
- These angles are supplementary.
- Answer: Supplementary angles.

##### Diagram 8:
- Two angles are shown, and their measures add up to 90° (one is labeled as 55°, and the other is implied to be 35°).
- These angles are complementary.
- Answer: Complementary angles.

##### Diagram 9:
- Two angles are shown, and their measures add up to 180° (one is labeled as 140°, and the other is implied to be 40°).
- These angles are supplementary.
- Answer: Supplementary angles.

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#### Part 2: Answering Questions Using the Figure at the Right

The figure shows five points \( A, B, C, D, E \) with intersecting lines forming various angles.

##### Question 10: Name two acute vertical angles.
- Vertical angles are opposite each other when two lines intersect.
- Acute angles are angles less than 90°.
- From the figure, the acute vertical angles are \( \angle AGE \) and \( \angle CGE \).
- Answer: \( \angle AGE \) and \( \angle CGE \).

##### Question 11: Name two obtuse vertical angles.
- Obtuse angles are angles greater than 90° but less than 180°.
- From the figure, the obtuse vertical angles are \( \angle AGF \) and \( \angle CGF \).
- Answer: \( \angle AGF \) and \( \angle CGF \).

##### Question 12: Name a pair of adjacent angles.
- Adjacent angles share a common vertex and a common side.
- From the figure, one pair of adjacent angles is \( \angle AGE \) and \( \angle EGD \).
- Answer: \( \angle AGE \) and \( \angle EGD \).

##### Question 13: Name a pair of complementary angles.
- Complementary angles add up to 90°.
- From the figure, no pair of angles explicitly adds up to 90°. However, if we assume the angles are measured, we can identify them.
- For example, if \( \angle AGE = 30^\circ \) and \( \angle EGD = 60^\circ \), then they are complementary.
- Answer: \( \angle AGE \) and \( \angle EGD \) (assuming their measures add up to 90°).

##### Question 14: Name an angle supplementary to \( \angle AGF \).
- Supplementary angles add up to 180°.
- From the figure, \( \angle AGF \) and \( \angle FGE \) are supplementary because they form a straight line.
- Answer: \( \angle FGE \).

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Final Answers:

1. Adjacent
2. Vertical
3. Supplementary
4. Complementary
5. Supplementary
6. Complementary
7. Supplementary
8. Complementary
9. Supplementary

10. \( \angle AGE \) and \( \angle CGE \)
11. \( \angle AGF \) and \( \angle CGF \)
12. \( \angle AGE \) and \( \angle EGD \)
13. \( \angle AGE \) and \( \angle EGD \) (assuming complementary)
14. \( \angle FGE \)

\boxed{Adjacency, Verticality, Supplementary, Complementary}