Practice worksheet for finding missing vertical angles and identifying congruent and supplementary angles.

Since I can't view or access images directly, I’ll help you solve the problem based on the description of the task. From your message, it appears to be a geometry worksheet focused on vertical angles, congruent angles, and supplementary angles, with diagrams involving intersecting lines.

Let me walk through how to solve this step-by-step based on typical problems like this. If you can describe the diagram or provide more details (e.g., angle measures shown), I can give exact answers. But here’s a general guide:

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🔷 Part 1: Understanding the Concepts

- Vertical Angles: When two lines intersect, they form two pairs of opposite angles called *vertical angles*. These are always congruent (equal in measure).
- Supplementary Angles: Two angles that add up to 180°.
- Congruent Angles: Angles that have the same measure.

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🔷 Step 1: Use the Diagram to Fill Out the Chart

Assuming there are multiple intersecting lines forming various angles labeled 1 through 12 or so, we need to use relationships:

#### Example:
If two lines cross, they create four angles:
- Let’s say angle 1 = 50°
- Then its vertical angle (opposite) is also 50°
- The adjacent angles are supplementary → 180° – 50° = 130°

So:
- Angle 1 = 50°
- Vertical angle (say angle 3) = 50°
- Adjacent angles (angles 2 and 4) = 130° each

You would repeat this logic for all angles.

> ✔ Rule: Vertical angles are equal; adjacent angles on a straight line sum to 180°.

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🔷 Step 2: Answer the Questions

#### 1. Name a pair of congruent angles.
- Any pair of vertical angles.
- Example: ∠1 and ∠3 (if they’re opposite each other)
- Or: ∠2 and ∠4

✔ Answer: ∠1 and ∠3

#### 2. How many pairs of congruent angles are in the diagram?
- Each intersection of two lines creates two pairs of vertical angles.
- So if there are n intersections, then total pairs = 2 × n

👉 For example, if there are three sets of intersecting lines:
- 3 intersections × 2 pairs = 6 pairs of congruent angles

But if only one intersection, then 2 pairs.

✔ Answer: 2 pairs (assuming one intersection)

#### 3. Name a pair of supplementary angles.
- Any two angles that form a straight line (adjacent angles at an intersection).
- Example: ∠1 and ∠2 (they are next to each other and form a line)

✔ Answer: ∠1 and ∠2

#### 4. Assume the measure of angle 2 is 70° and angle 2 is congruent to angle 5. Find the other angle measures in the diagram.

Let’s break this down:

- Given: ∠2 = 70°
- ∠2 ≅ ∠5 → So ∠5 = 70°
- Now, find other angles using relationships.

Assume the diagram has multiple intersecting lines.

##### First Intersection (with ∠2):
- If ∠2 = 70°, then its vertical angle = 70°
- Its adjacent angles = 180° – 70° = 110°

So:
- ∠2 = 70°
- Vertical angle (say ∠1) = 70°
- Adjacent angles (∠3 and ∠4) = 110° each

Now, since ∠5 = 70°, and it's congruent to ∠2, maybe ∠5 is at another intersection.

If ∠5 = 70°, then:
- Its vertical angle = 70°
- Adjacent angles = 110°

So, depending on how many intersections, you can label all angles accordingly.

✔ Summary:
- ∠2 = 70°
- ∠5 = 70°
- Their vertical angles = 70°
- Adjacent angles = 110°
- All other angles follow from these

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🔷 Final Tips

To complete the chart:
| Angle | Measure |
|-------|--------|
| 1 | 70° |
| 2 | 70° |
| 3 | 110° |
| 4 | 110° |
| 5 | 70° |
| 6 | 70° |
| ... | ... |

(Adjust based on actual diagram layout.)

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✔ Final Answers (Example):

1. A pair of congruent angles: ∠1 and ∠3
2. Number of pairs of congruent angles: 2 pairs (if one intersection)
3. A pair of supplementary angles: ∠1 and ∠2
4. With ∠2 = 70° and ∠5 = 70°:
- Vertical angles to ∠2 and ∠5: 70°
- Adjacent angles: 110°
- All others follow from these

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🔍 Note: If you can describe the diagram (number of lines, labels, known angle measures), I can give exact values and fill in the chart precisely.

Would you like to describe the diagram now?