Angle Vocabulary | PDF - Free Printable

It looks like you've uploaded an image of a worksheet or educational material about angle relationships formed when a transversal intersects two parallel lines. The table in the image defines several types of angles, including:

- Exterior Angles
- Same Side Interior Angles
- Same Side Exterior Angles
- Vertical Angles
- Corresponding Angles
- Complementary Angles
- Supplementary Angles

However, the task or problem you're referring to is not clearly visible in your description or image. You mentioned "I uploaded an image with a task," but there's no specific question or diagram shown here (e.g., finding missing angle measures, identifying angle pairs, etc.).

Let me help by explaining the concepts in the table and then guiding you on how to solve typical problems involving these angle relationships.

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🔍 Explanation of Angle Relationships:

1. Exterior Angles
- Angles located outside the two parallel lines.
- When a transversal cuts through two parallel lines, exterior angles on the same side are supplementary (add up to 180°), and alternate exterior angles are congruent.

2. Same Side Interior Angles
- These are inside the parallel lines and on the same side of the transversal.
- They are supplementary (sum to 180°).

3. Same Side Exterior Angles
- These are outside the parallel lines and on the same side of the transversal.
- Also supplementary (sum to 180°).

4. Vertical Angles
- Formed when two lines intersect.
- Opposite angles are equal (congruent).
- Example: If ∠1 and ∠2 are vertical angles, then ∠1 = ∠2.

5. Corresponding Angles
- Angles that are in the same relative position at each intersection.
- When lines are parallel, corresponding angles are congruent.

6. Complementary Angles
- Two angles that add up to 90°.
- Often found in right triangles or when a right angle is split.

7. Supplementary Angles
- Two angles that add up to 180°.
- Common in straight lines or adjacent angles forming a linear pair.

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✔ Typical Problem Type:

A common task might be:

> Given a diagram of two parallel lines cut by a transversal, find the measure of a missing angle.

#### Example:
Suppose one angle is given as 60°, and you're asked to find the measure of its corresponding angle.

- Since corresponding angles are equal, the answer is 60°.

Or if you're given a same-side interior angle of 110°, then the other angle must be:
- 180° – 110° = 70° (because they are supplementary).

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🛠️ How to Solve Such Problems:

1. Identify the type of angle relationship involved.
2. Use known rules:
- Corresponding → equal
- Alternate interior/exterior → equal
- Same side interior/exterior → supplementary (add to 180°)
- Vertical angles → equal
- Linear pairs → supplementary
3. Plug in known values and solve.

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❓ What’s Missing?

Since I can’t see the actual problem or diagram, I can't give a specific answer. But if you describe the problem (e.g., “Find angle x if two parallel lines are cut by a transversal and one angle is 120°”), I can walk you through it step-by-step.

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👉 Please provide:
- The exact question or diagram details.
- Or tell me what you're supposed to do (e.g., find missing angles, classify angle pairs, etc.).

Then I’ll solve it and explain clearly!