Geometry worksheet on angle pair relationships with diagrams and problems.

Problem Analysis:

The task involves identifying the relationships between angles in the first part and finding the measure of a specific angle in the second part. Let's solve each part step by step.

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Part 1: Name the relationship (complementary, linear pair, vertical, or adjacent)

#### 1)
- Description: Two angles are shown that share a common vertex and one side but do not overlap.
- Relationship: These angles are adjacent because they share a common vertex and a common side.

#### 2)
- Description: Two angles are shown that form a straight line.
- Relationship: These angles are a linear pair because they are adjacent and their non-common sides form a straight line.

#### 3)
- Description: Two angles are shown that share a common vertex but no common side.
- Relationship: These angles are vertical angles because they are opposite each other when two lines intersect.

#### 4)
- Description: Two angles are shown that share a common vertex and one side but do not overlap.
- Relationship: These angles are adjacent because they share a common vertex and a common side.

#### 5)
- Description: Two angles are shown within a triangle.
- Relationship: These angles are adjacent because they share a common vertex and a common side.

#### 6)
- Description: Two angles are shown that share a common vertex and one side but do not overlap.
- Relationship: These angles are adjacent because they share a common vertex and a common side.

#### 7)
- Description: Two angles are shown within a triangle.
- Relationship: These angles are adjacent because they share a common vertex and a common side.

#### 8)
- Description: Two angles are shown that are opposite each other when two lines intersect.
- Relationship: These angles are vertical angles because they are opposite each other when two lines intersect.

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Part 2: Find the measure of angle \( b \)

#### 9)
- Description: Angle \( b \) is given as supplementary to a \( 20^\circ \) angle.
- Solution: Supplementary angles add up to \( 180^\circ \).
\[
b + 20^\circ = 180^\circ
\]
\[
b = 180^\circ - 20^\circ = 160^\circ
\]
- Answer: \( b = 160^\circ \)

#### 10)
- Description: Angle \( b \) is given as vertical to a \( 65^\circ \) angle.
- Solution: Vertical angles are congruent.
\[
b = 65^\circ
\]
- Answer: \( b = 65^\circ \)

#### 11)
- Description: Angle \( b \) is given as complementary to a \( 65^\circ \) angle.
- Solution: Complementary angles add up to \( 90^\circ \).
\[
b + 65^\circ = 90^\circ
\]
\[
b = 90^\circ - 65^\circ = 25^\circ
\]
- Answer: \( b = 25^\circ \)

#### 12)
- Description: Angle \( b \) is given as an exterior angle to a triangle with interior angles \( 63^\circ \) and \( 29^\circ \).
- Solution: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
\[
b = 63^\circ + 29^\circ = 92^\circ
\]
- Answer: \( b = 92^\circ \)

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Final Answers:

1. Adjacent
2. Linear pair
3. Vertical
4. Adjacent
5. Adjacent
6. Adjacent
7. Adjacent
8. Vertical

9. \( b = 160^\circ \)
10. \( b = 65^\circ \)
11. \( b = 25^\circ \)
12. \( b = 92^\circ \)

\boxed{
\text{Part 1: Adjacent, Linear pair, Vertical, Adjacent, Adjacent, Adjacent, Adjacent, Vertical}
}
\boxed{
\text{Part 2: } 160^\circ, 65^\circ, 25^\circ, 92^\circ
}