Corresponding Angles Worksheets - Free Printable

Let's solve each of these problems step by step using the properties of corresponding angles, supplementary angles, and parallel lines cut by a transversal.

When two parallel lines are cut by a transversal, several angle relationships apply:

- Corresponding angles are equal.
- Alternate interior angles are equal.
- Same-side interior angles are supplementary (add to 180°).
- Vertical angles are equal.
- Linear pairs add up to 180°.

We'll go through each figure one at a time.

---

1)

```
←───────────→
146° 34°
\ /
\ /
x
```

The angle marked 34° is adjacent to x, and together they form a straight line with the 146° angle.

But wait — let’s analyze carefully.

Actually, the two parallel lines are horizontal. A transversal cuts them forming angles.

From the diagram:
- The top angle on the upper line is 146° and 34°.
- Since 146° + 34° = 180°, they are on a straight line → so the transversal makes a straight angle.

Now, x is an angle on the lower line, corresponding to the 34° angle.

Since the lines are parallel, corresponding angles are equal.

So, x = 34°

✔ Answer: x = 34°

---

2)

```
↑ ↑
| |
| 93° |
| |
↓ ↓
←────→
87°
x
```

Wait — this looks like a transversal crossing two vertical lines? But the arrows suggest the horizontal lines are the parallels.

Actually, the vertical lines might be the parallel lines? Let's interpret.

Wait — the arrows on the left and right sides point up/down, suggesting the vertical lines are parallel.

But the transversal is horizontal.

Angles given:
- Top angle: 93°
- Bottom angle: 87°
- x is labeled at the bottom-left

Wait — the diagram shows:

- Two vertical parallel lines.
- A horizontal transversal cutting them.
- At the top, between the transversal and the right line: 93°
- At the bottom, between the transversal and the left line: 87°, and x is the other angle there.

But since the transversal is horizontal, and the lines are vertical, then the angles formed should be:

- On the right side: 93° above the transversal.
- On the left side: below the transversal, we have 87° and x.

But 87° and x are adjacent angles forming a straight line? Or are they vertical?

Wait — likely, x and 87° are vertical angles or adjacent?

Looking again: probably the 87° and x are on opposite sides of the transversal, but same line.

Wait — actually, from standard notation, if two parallel lines are cut by a transversal, then:

- The angle 93° is on the right line, above the transversal.
- Then, the corresponding angle on the left line, above the transversal, would also be 93°.

But we’re told the angle below on the left is 87°, and x is next to it.

Wait — maybe the 87° and x are on the same side?

Alternatively, perhaps x is equal to 93° because it's a corresponding angle.

But the 87° might be not on the same transversal.

Wait — better to assume:

- The 93° angle is on the right line, above the transversal.
- The x is on the left line, above the transversal — so it's corresponding to 93° → so x = 93°

But why is 87° there?

Ah — maybe 87° is the angle below on the left line?

Then, x is above on the left line.

So, x and 87° are on the same line, forming a straight angle?

No — unless the transversal is straight.

Wait — perhaps the 87° is adjacent to x?

But that would mean x + 87° = 180° → x = 93°

Yes! That matches.

So, if x and 87° are adjacent on a straight line, then:

x = 180° - 87° = 93°

And also, the 93° on the right corresponds to x, so both give x = 93°

✔ Answer: x = 93°

---

3)

```
←───────────→
75° 105°
\ /
\ /
x
```

Two parallel horizontal lines, transversal crosses them.

Top line: angles 75° and 105° — they sum to 180° → so they are on a straight line.

So the transversal forms a 75° and 105° angle on the top.

On the bottom line, x is the angle corresponding to 75° or 105°?

If x is in the same position as 75°, then it's corresponding → x = 75°

But let's see: the 75° is on the left side, above the transversal.

Then, x is on the left side, below the transversal.

So it's not corresponding — it's alternate interior?

Wait — no: alternate interior would be on opposite sides and inside.

But here, x is on the same side as 75°, but below.

So x and 75° are corresponding only if they're in the same relative position.

Wait — actually, x is below and left, while 75° is above and left — so they are vertical angles? No.

Wait — better to think: the 105° is on the right, above.

Then x is on the left, below.

But notice: 75° and 105° are adjacent on the top line → 75+105=180 → so they are supplementary.

Now, x is opposite to the 75° angle — meaning it's vertically opposite?

Wait — no. The transversal crosses the top line at 75° and 105°.

Then, on the bottom line, the corresponding angle to 75° would be x, if it's in the same corner.

But from the diagram, x is on the bottom, left, and the 75° is on the top, left — so yes, they are corresponding angles.

Therefore, x = 75°

✔ Answer: x = 75°

---

4)

```
↑ ↑
| |
| x |
| |
↓ ↓
←────→
111°
```

Two vertical parallel lines, horizontal transversal.

Angle on the bottom of the left line: 111°

Angle on the top of the left line: x

They are on a straight line → so they are supplementary.

So:
x + 111° = 180°
→ x = 69°

Also, 111° is on the bottom of the left line. Its corresponding angle on the right line, bottom, would also be 111°.

But we don’t need that.

So x = 69°

✔ Answer: x = 69°

---

5)

```
←───────────→
x
\
\
\
←────→
150°
\
\
30°
```

This is tricky.

We have two parallel horizontal lines, cut by a transversal that goes down to the right.

On the bottom line, we have 150° and 30° — but they are adjacent?

Wait — the 150° is on the left, and 30° is on the right, but both on the bottom line?

But 150 + 30 = 180 → so they are on a straight line.

So the transversal makes a 150° angle with the bottom line on the left, and 30° on the right.

But x is on the top line, left side.

So x is corresponding to the 150° angle?

Yes — same position: top-left vs bottom-left.

So x = 150°

But wait — is the transversal going down-right? So the angle on the top line, left side, would be corresponding to the bottom-left angle.

So x = 150°

✔ Answer: x = 150°

---

6)

```
↑ ↑
| |
| x |
| |
↓ ↓
←────→
52°
```

Similar to #4.

Two vertical parallel lines, horizontal transversal.

Angle on the bottom of the right line: 52°

Angle on the top of the right line: x

They are adjacent on a straight line → supplementary.

So:
x + 52° = 180°
→ x = 128°

✔ Answer: x = 128°

---

7)

```
←───────────→
x
\
\
\
←────→
131°
\
\
49°
```

Parallel lines: top and bottom horizontal.

Transversal cuts them.

On the bottom line, we have 131° and 49° — adjacent angles?

131 + 49 = 180 → yes, so they are on a straight line.

So the transversal makes 131° on the left side of the bottom line.

Then x is on the top line, left side.

So x is corresponding to 131° → x = 131°

✔ Answer: x = 131°

---

8)

```
↑ ↑
| |
| x |
| |
↓ ↓
←────→
103°
\
\
\
77°
```

Two vertical parallel lines, horizontal transversal.

On the right line, we have 103° and 77° — are they adjacent?

103 + 77 = 180 → yes, so they are on a straight line.

So the 103° is on the top of the right line.

Then x is on the top of the left line.

So x is corresponding to 103° → x = 103°

✔ Answer: x = 103°

---

9)

```
←───────────→
x
\
\
\
←────→
114°
\
\
66°
```

Two horizontal parallel lines.

Transversal cuts them.

On the bottom line: 114° and 66° — adjacent? 114 + 66 = 180 → yes.

So 114° is on the left side of the bottom line.

Then x is on the top line, left side.

So x is corresponding to 114° → x = 114°

✔ Answer: x = 114°

---

## ✔ Final Answers:

1) x = 34°
2) x = 93°
3) x = 75°
4) x = 69°
5) x = 150°
6) x = 128°
7) x = 131°
8) x = 103°
9) x = 114°

Let me know if you'd like diagrams explained further!