Worksheet on angle relationships including vertical, adjacent, complementary, and supplementary angles.

Since I can't view or access uploaded images directly, I can’t see the specific angles or figures in your worksheet. However, I can help you solve the problems based on common angle relationship tasks like the ones described in your worksheet.

Let me walk you through how to approach each section of the worksheet and provide explanations for typical problems of this type. You can then apply these concepts to your image.

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Section 1: Name the Relationship – Vertical, Adjacent, Complementary, or Supplementary

Definitions:
- Vertical angles: Angles opposite each other when two lines intersect. They are always equal.
- Adjacent angles: Angles that share a common vertex and side but do not overlap.
- Complementary angles: Two angles that add up to 90°.
- Supplementary angles: Two angles that add up to 180°.

How to identify:
1. Look at the position of the angles:
- If they are opposite each other → vertical
- If they are next to each other with a shared side → adjacent
2. Check their sum:
- If they add to 90° → complementary
- If they add to 180° → supplementary

> 🔎 Example: If two angles form a straight line, they are supplementary (sum = 180°). If they form a right angle together, they are complementary (sum = 90°).

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Section 2: Identify All Linear Pairs in Each Figure

A linear pair consists of two adjacent angles that form a straight line (i.e., their non-common sides form a straight line). The sum is always 180°.

Steps:
1. Find angles that are next to each other and form a straight line.
2. List all such pairs.

> 🔎 Example: In a figure with four angles around a point where two lines cross, there are typically 4 linear pairs (e.g., ∠1 & ∠2, ∠2 & ∠3, etc.).

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Section 3: Find the Measure of Angle θ

This usually involves using angle relationships:

#### Common Types:
1. Linear Pair: If angle θ and another angle form a straight line:
$$
\theta + \text{other angle} = 180^\circ
\Rightarrow \theta = 180^\circ - \text{other angle}
$$

2. Vertical Angles: If θ is vertical to a known angle:
$$
\theta = \text{measure of vertical angle}
$$

3. Complementary Angles: If θ and another angle make 90°:
$$
\theta = 90^\circ - \text{other angle}
$$

4. Triangle Angles: If θ is part of a triangle, use:
$$
\text{Sum of interior angles} = 180^\circ
$$

5. Parallel Lines & Transversals: Use corresponding, alternate interior, or same-side interior angle rules.

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✔ Let’s Solve an Example Problem (Typical from This Worksheet):

#### Example:
In a figure, two lines intersect, forming four angles. One angle is labeled 60°. Find the measure of angle θ opposite it.

Solution:
- The angle opposite the 60° angle is vertical to it.
- Vertical angles are congruent.
- So, $ \theta = 60^\circ $

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#### Another Example:
Two angles form a straight line. One is 120°. Find θ.

Solution:
- They form a linear pair, so they are supplementary.
- $ \theta = 180^\circ - 120^\circ = 60^\circ $

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Final Tips:

- Label all known angles.
- Use properties:
- Vertical angles = equal
- Linear pairs = 180°
- Complementary = 90°
- Supplementary = 180°
- Always check if angles are adjacent, vertical, or part of a triangle/parallel lines.

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If you can describe the figures or give the angle measures from the image (e.g., “in figure 7, one angle is 130°, and θ is opposite”), I can help you solve them step-by-step.

Just let me know what’s in the image!