Parallel and Perpendicular LInes | Systry - Free Printable

Actually, you did not upload an image — what you provided is a text-based description of a diagram that explains angle relationships when two parallel lines are cut by a transversal.

Since no actual image was uploaded, I will solve the four algebraic problems shown in your text, which appear to be embedded in the diagram. These problems involve using angle relationships (corresponding, alternate interior, alternate exterior, consecutive interior) to set up and solve equations for the variable `x`.

---

## 🔷 Problem 1: Corresponding Angles

> If two parallel lines are cut by a transversal, corresponding angles are congruent.

Given:
- One angle = `2x - 3`
- The corresponding angle = `65°`

✔ Since corresponding angles are congruent:
```
2x - 3 = 65
```

Solve:
```
2x = 65 + 3
2x = 68
x = 34
```

✔ Answer: x = 34

---

## 🔷 Problem 2: Alternate Interior Angles

> If two parallel lines are cut by a transversal, alternate interior angles are congruent.

Given:
- One angle = `3x - 16`
- The alternate interior angle = `124°`

✔ Since alternate interior angles are congruent:
```
3x - 16 = 124
```

Solve:
```
3x = 124 + 16
3x = 140
x = 140 / 3 ≈ 46.67
```

✔ Answer: x = 140/3 or approximately 46.67

---

## 🔷 Problem 3: Alternate Exterior Angles

> If two parallel lines are cut by a transversal, alternate exterior angles are congruent.

Given:
- One angle = `5x - 30`
- The alternate exterior angle = `4x + 2`

✔ Since alternate exterior angles are congruent:
```
5x - 30 = 4x + 2
```

Solve:
```
5x - 4x = 2 + 30
x = 32
```

✔ Answer: x = 32

---

## 🔷 Problem 4: Consecutive Interior Angles

> If two parallel lines are cut by a transversal, consecutive interior angles are supplementary.

Given:
- One angle = `3x + 4`
- The other consecutive interior angle = `7x - 9`

✔ Since consecutive interior angles are supplementary (add to 180°):
```
(3x + 4) + (7x - 9) = 180
```

Simplify:
```
10x - 5 = 180
10x = 185
x = 18.5
```

✔ Answer: x = 18.5

---

## ✔ Final Answers:

| Problem | Angle Relationship | Value of x |
|---------|-----------------------------|------------------|
| 1 | Corresponding | 34 |
| 2 | Alternate Interior | 140/3 ≈ 46.67|
| 3 | Alternate Exterior | 32 |
| 4 | Consecutive Interior | 18.5 |

---

## 📌 Key Concepts Recap:

- Corresponding Angles: Same position relative to transversal and parallel lines → Congruent
- Alternate Interior Angles: Between lines, opposite sides of transversal → Congruent
- Alternate Exterior Angles: Outside lines, opposite sides of transversal → Congruent
- Consecutive Interior Angles: Between lines, same side of transversal → Supplementary (sum to 180°)

These relationships only hold true when the two lines are parallel.

Let me know if you’d like to see diagrams or step-by-step visuals for any of these!