Practice worksheet for calculating unknown vertical angles using geometric relationships.

Let's solve each problem on the Vertical Angles worksheet step by step.

---

🔷 What are Vertical Angles?

Vertical angles are the angles opposite each other when two lines intersect. They are always congruent (equal in measure).

Also, adjacent angles formed by intersecting lines are supplementary, meaning they add up to 180°.

---

We'll go through each question:

---

Problem 1

Given:
- ∠1 = 132°

We need to find:
- m∠1 = 132° (given)
- m∠2 = ?
- m∠3 = ?
- m∠4 = ?

From the diagram:
- ∠1 and ∠3 are vertical angles → so ∠3 = ∠1 = 132°
- ∠2 and ∠4 are vertical angles
- ∠1 and ∠2 are adjacent → supplementary → ∠1 + ∠2 = 180°

So:
- ∠2 = 180° - 132° = 48°
- ∠4 = ∠2 = 48° (vertical angles)

✔ Answers:
- m∠1 = 132°
- m∠2 = 48°
- m∠3 = 132°
- m∠4 = 48°

---

Problem 2

Given:
- ∠2 = 19°

Find:
- m∠1 = ?
- m∠2 = 19° (given)
- m∠3 = ?
- m∠4 = ?

From diagram:
- ∠1 and ∠3 are vertical angles
- ∠2 and ∠4 are vertical angles → ∠4 = ∠2 = 19°
- ∠1 and ∠2 are adjacent → supplementary

So:
- ∠1 = 180° - 19° = 161°
- ∠3 = ∠1 = 161°

✔ Answers:
- m∠1 = 161°
- m∠2 = 19°
- m∠3 = 161°
- m∠4 = 19°

---

Problem 3

Given:
- ∠1 = 25°

Find:
- m∠1 = 25°
- m∠2 = ?
- m∠3 = ?
- m∠4 = ?

From diagram:
- ∠1 and ∠3 are vertical angles → ∠3 = 25°
- ∠2 and ∠4 are vertical angles
- ∠1 and ∠2 are adjacent → supplementary

So:
- ∠2 = 180° - 25° = 155°
- ∠4 = ∠2 = 155°

✔ Answers:
- m∠1 = 25°
- m∠2 = 155°
- m∠3 = 25°
- m∠4 = 155°

---

Problem 4

Given:
- ∠1 = 10°

Find:
- m∠1 = 10°
- m∠2 = ?
- m∠3 = ?
- m∠4 = ?

From diagram:
- ∠1 and ∠3 are vertical → ∠3 = 10°
- ∠2 and ∠4 are vertical
- ∠1 and ∠2 are adjacent → supplementary

So:
- ∠2 = 180° - 10° = 170°
- ∠4 = ∠2 = 170°

✔ Answers:
- m∠1 = 10°
- m∠2 = 170°
- m∠3 = 10°
- m∠4 = 170°

---

Problem 5

Given:
- ∠1 = 127°

Find:
- m∠1 = 127°
- m∠2 = ?
- m∠3 = ?
- m∠4 = ?

From diagram:
- ∠1 and ∠3 are vertical → ∠3 = 127°
- ∠2 and ∠4 are vertical
- ∠1 and ∠2 are adjacent → supplementary

So:
- ∠2 = 180° - 127° = 53°
- ∠4 = ∠2 = 53°

✔ Answers:
- m∠1 = 127°
- m∠2 = 53°
- m∠3 = 127°
- m∠4 = 53°

---

Problem 6

Given:
- ∠1 = 113°

Find:
- m∠1 = 113°
- m∠2 = ?
- m∠3 = ?
- m∠4 = ?

From diagram:
- ∠1 and ∠3 are vertical → ∠3 = 113°
- ∠2 and ∠4 are vertical
- ∠1 and ∠2 are adjacent → supplementary

So:
- ∠2 = 180° - 113° = 67°
- ∠4 = ∠2 = 67°

✔ Answers:
- m∠1 = 113°
- m∠2 = 67°
- m∠3 = 113°
- m∠4 = 67°

---

✔ Final Answer Summary:

| Problem | m∠1 | m∠2 | m∠3 | m∠4 |
|--------|---------|---------|---------|---------|
| 1 | 132° | 48° | 132° | 48° |
| 2 | 161° | 19° | 161° | 19° |
| 3 | 25° | 155° | 25° | 155° |
| 4 | 10° | 170° | 10° | 170° |
| 5 | 127° | 53° | 127° | 53° |
| 6 | 113° | 67° | 113° | 67° |

---

📝 Explanation Recap:

- Vertical angles are equal → use that to find opposite angles.
- Adjacent angles are supplementary → sum to 180°.
- Use these two rules together to find all missing angles.

Let me know if you'd like a printable version or explanation for a specific problem!