Corresponding Angles Worksheets - Free Printable

Let’s solve each problem one by one. Remember: when two parallel lines are cut by a transversal, corresponding angles are equal. Also, angles on a straight line add up to 180°, and vertical angles are equal.

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Problem 1)
We see two parallel lines cut by a transversal. The angle labeled 54° is corresponding to the angle next to x (on the same side of the transversal). But wait — actually, look at the top line: there’s a 146° angle and a 34° angle next to it. Since they’re on a straight line:
146° + 34° = 180° → that checks out.
Now, the 34° angle and the angle marked “x” are vertical angles? No — let’s think again. Actually, the 34° angle and the angle directly below it (on the lower parallel line) are corresponding angles, so they should be equal. But in the diagram, the angle labeled “x” is adjacent to the 34° angle on the lower line? Wait — no, looking carefully: the transversal cuts both lines. The 34° is above the top line, and x is below the bottom line, on the same side. So they are corresponding angles!
→ Therefore, x = 34°

Wait — but let me double-check. If the 34° is on the top right, then the corresponding angle on the bottom right would also be 34°. And if x is that angle, then yes. But in the diagram, x is written inside the lower intersection, on the left side? Hmm — maybe I misread.

Actually, let’s use another approach. At the top intersection: we have 146° and 34° forming a straight line → correct. The 146° angle has a vertical angle opposite it — which would also be 146°. Then, the angle corresponding to that 146° on the lower line would be the one on the same side — which might be x? Or maybe not.

Alternatively, notice that the 34° angle and the angle marked x are alternate interior angles? Let’s sketch mentally:

Top line: transversal comes down from left to right. Angle between top line and transversal on the right is 34°. On the bottom line, the angle between bottom line and transversal on the left is x. That would make them alternate interior → so equal? Yes! Alternate interior angles are equal when lines are parallel.

So if 34° is on top right, and x is on bottom left — those are alternate interior → x = 34°.

But wait — in standard position, if the transversal slants down to the right, then:

- Top right angle: 34°
- Bottom left angle: x → these are alternate interior → equal → x = 34°

Yes. So x = 34

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Problem 2)
Two vertical parallel lines, cut by a horizontal transversal. We’re given 93° and 87° on the right side. Note: 93° + 87° = 180° → they form a straight line, good.

The angle x is on the left side, same level as the 93° angle. Since the lines are parallel, the angle corresponding to 93° on the left side should also be 93°? But wait — actually, the 93° and x are on opposite sides of the transversal, but same relative position? Let’s think.

Actually, the 93° angle and the angle vertically opposite to x are corresponding? Maybe easier: the angle adjacent to x on the left side (same vertex) should correspond to the 87° angle on the right? Because 87° is below the transversal on the right, so its corresponding angle on the left would be below the transversal — which is adjacent to x.

Since 87° corresponds to the angle next to x (on the left, below), then that angle is 87°. Then, since x and that 87° angle are on a straight line (vertical line), they add to 180°.

So: x + 87° = 180° → x = 93°

Alternatively, x and the 93° angle are vertical angles? No — they’re on different lines.

Wait — actually, the 93° angle and x are corresponding angles? Let’s see: both are above the transversal, and on the left/right respectively? No — corresponding means same relative position. If 93° is above the transversal on the right line, then the corresponding angle on the left line would be above the transversal — which is exactly where x is? In the diagram, x is drawn on the left line, above the transversal? Looking back: in problem 2, the arrows show vertical lines, horizontal transversal. The 93° is on the right line, above the transversal. The 87° is on the right line, below. On the left line, x is shown above the transversal. So yes — x and 93° are both above the transversal, on their respective lines → corresponding angles → so x = 93°

But earlier I thought x + 87 = 180 → that would be if x were adjacent to the corresponding of 87. But if x is corresponding to 93, then x=93.

And indeed, 93° and 87° are supplementary, which makes sense for adjacent angles on a straight line.

So x = 93

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Problem 3)
Parallel lines cut by a transversal. Given 75° and 105° on the top line. Check: 75+105=180 → good.

Angle x is on the bottom line, on the same side as the 105° angle? Let’s see: the 105° is on the top right, so the corresponding angle on the bottom right would be equal to 105°. But in the diagram, x is drawn on the bottom left? Or bottom right?

Looking at the description: "75° 105°" on top, and x on bottom. Typically, if 105° is on the top right, then the corresponding angle on the bottom right is also 105°. But if x is on the bottom left, then it might be corresponding to 75°.

Assume the transversal is going down to the right. Top line: left angle 75°, right angle 105°. Bottom line: left angle x, right angle ?

Then, the 75° (top left) corresponds to the bottom left angle → so x = 75°

Yes, because corresponding angles are in the same relative position. So x = 75

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Problem 4)
Vertical parallel lines, transversal cutting diagonally. Given 69° and 111° on the right side. 69+111=180 → good.

Angle x is on the left side. Now, the 69° is above the transversal on the right line. Its corresponding angle on the left line would be above the transversal — which is where x is? In the diagram, x is likely on the left, above the transversal.

So corresponding angles: x corresponds to 69° → x = 69°

But let’s confirm: if 69° is top-right, then top-left should be equal if corresponding? Yes.

Alternatively, the 111° is below on the right, so its corresponding angle on the left below would be 111°, and x is above, so x + 111° = 180°? Only if they are adjacent on the straight line.

In this case, since the lines are vertical, and transversal is diagonal, at each intersection, the angles around the point sum to 360°, but on a straight line (the vertical line), adjacent angles sum to 180°.

At the left intersection: the vertical line has two angles: x (say, upper) and another below. They must sum to 180°.

What is the angle below x? It corresponds to the 111° on the right (since both are below the transversal). So that angle is 111°. Thus, x + 111° = 180° → x = 69°

Same answer. So x = 69

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Problem 5)
Parallel lines, transversal. Given 150° and 30° on the bottom line. 150+30=180 → good.

Angle x is on the top line. Now, the 30° is on the bottom right. Its corresponding angle on the top right would be 30°. But x is on the top left? Or top right?

Typically, if 30° is bottom right, then top right corresponding is 30°. But if x is on the top left, then it corresponds to the bottom left angle.

Bottom left angle: since bottom line has 150° on left and 30° on right, so bottom left is 150°. Then corresponding top left is also 150°. So if x is top left, x=150°.

But in many diagrams, x is placed where the acute angle is. Let me think differently.

Notice that the 30° angle and the angle vertically opposite to x might be related.

Actually, the 30° angle and x are alternate exterior angles? Or perhaps consecutive interior.

Another way: the angle adjacent to x on the top line (same vertex) should be equal to the 30° angle if they are corresponding? Let's define positions.

Assume transversal goes down to the right. Bottom line: left angle 150°, right angle 30°. Top line: left angle x, right angle y.

Then, the 30° (bottom right) corresponds to y (top right) → y=30°.

Then, on the top line, x and y are on a straight line → x + y = 180° → x + 30° = 180° → x = 150°

Yes. So x = 150

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Problem 6)
Vertical parallel lines, transversal. Given 128° and 52° on the right side. 128+52=180 → good.

Angle x is on the left side. Now, 128° is above the transversal on the right. Its corresponding angle on the left above would be 128°. But if x is below on the left, then it corresponds to 52°.

In the diagram, x is likely on the left, below the transversal? Or above? The problem says "x" is at the intersection on the left.

Assume: right side, above transversal: 128°, below: 52°. Left side, above: ?, below: x.

Then, the 52° (right below) corresponds to x (left below) → so x = 52°

Because corresponding angles are equal.

To confirm: the 128° corresponds to the angle above on the left, say z. Then z=128°, and x + z = 180° (since on straight vertical line) → x + 128° = 180° → x=52°. Same thing.

So x = 52

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Problem 7)
Parallel lines, transversal. Given 131° and 49° on the bottom line. 131+49=180 → good.

Angle x is on the top line. Similar to problem 5.

Bottom left: 131°, bottom right: 49°.

Corresponding angles: top left corresponds to bottom left → so if x is top left, x=131°.

Top right corresponds to bottom right → 49°.

If x is on the top left, then x=131°.

But sometimes x is placed at the acute angle. However, based on standard labeling, and since 131° is obtuse, likely x is the other one.

Wait — in the diagram description, it might be that x is on the top, and the transversal is such that x is adjacent to the corresponding of 49°.

Let’s calculate: suppose x is on the top right. Then it corresponds to bottom right 49° → x=49°.

But how do we know? Perhaps from the position.

Notice that the 49° angle and x might be vertical or something.

Another approach: the angle vertically opposite to the 131° is also 131°, and that might be corresponding to x? Not necessarily.

Perhaps x and the 49° are alternate interior.

Let me assume the transversal is going down to the right. Bottom line: left 131°, right 49°. Top line: left ?, right x.

Then, the 49° (bottom right) and x (top right) are corresponding → x=49°.

Yes, that makes sense. Because if you go from bottom right to top right, same side, same relative position.

So x = 49

But let's verify with straight line: on top line, if x=49°, then the other angle is 131°, which corresponds to bottom left 131° — perfect.

So x=49.

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Problem 8)
Vertical parallel lines, transversal. Given 103° and 77° on the right side. 103+77=180 → good.

Angle x is on the left side. Now, 103° is above the transversal on the right. Its corresponding angle on the left above would be 103°. But if x is below on the left, then it corresponds to 77°.

In the diagram, x is likely on the left, below the transversal? Or the angle marked x is at the intersection.

Assume: right side, above: 103°, below: 77°. Left side, above: ?, below: x.

Then, 77° (right below) corresponds to x (left below) → x=77°.

Confirm: the 103° corresponds to the angle above on the left, say y=103°. Then x + y = 180° → x + 103° = 180° → x=77°. Yes.

So x = 77

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Problem 9)
Parallel lines, transversal. Given 114° and 66° on the bottom line. 114+66=180 → good.

Angle x is on the top line. Similar to others.

Bottom left: 114°, bottom right: 66°.

Corresponding angles: top left corresponds to bottom left → 114°.

Top right corresponds to bottom right → 66°.

If x is on the top right, then x=66°.

But how is x positioned? In many cases, x is the acute angle, but here 66° is acute, 114° obtuse.

Perhaps from the diagram, x is on the top, and the transversal is such that x is adjacent to the 114° corresponding.

Assume x is on the top right. Then it corresponds to bottom right 66° → x=66°.

Yes. To confirm, the other angle on top would be 114°, matching bottom left.

So x = 66

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Now, let's list all answers:

1) 34
2) 93
3) 75
4) 69
5) 150
6) 52
7) 49
8) 77
9) 66

I think I have them all. Let me quickly recap to ensure no mistakes.

For problem 1: alternate interior or corresponding — got 34, seems correct.

Problem 2: corresponding to 93° — yes.

Problem 3: corresponding to 75° — yes.

Problem 4: corresponding to 69° or via supplement — 69.

Problem 5: x=150, since it's supplementary to the corresponding of 30° — yes.

Problem 6: x=52, corresponding to 52° or supplement of 128° — yes.

Problem 7: x=49, corresponding to 49° — yes.

Problem 8: x=77, corresponding to 77° — yes.

Problem 9: x=66, corresponding to 66° — yes.

All seem consistent.

Final Answer:
1) 34
2) 93
3) 75
4) 69
5) 150
6) 52
7) 49
8) 77
9) 66