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 with a transversal. The angle labeled 34° 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 an angle of 146° and 34° next to it. Since they’re on a straight line:
146° + 34° = 180° → that checks out.
Now, the angle marked x is vertically opposite to the 34° angle? 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, x is shown as the angle that forms a linear pair with the 146° angle on the lower line? Wait — no, looking carefully:
Actually, the 34° angle and the angle marked x are vertical angles? Not quite. Let me reorient.

Better approach: On the upper line, we have 146° and 34° adjacent → sum to 180°, good.
The angle that corresponds to the 34° angle (same position relative to transversal and parallel lines) is the angle just above x on the lower line. So that angle is also 34°. Then, since x and that 34° angle form a straight line with the other angle? Wait — no.

Actually, simpler: The angle marked x is vertically opposite to the 34° angle? Let’s check positions.

Wait — perhaps I’m overcomplicating. Look: the 34° angle and the angle marked x are alternate interior angles? Or maybe corresponding?

Actually, here’s the key: The 34° angle and the angle immediately to the left of x (on the lower line) are corresponding angles → so that angle is 34°. Then, since x and that 34° angle are on a straight line with the 146° angle? No.

Wait — better: In figure 1, the transversal cuts both lines. The angle labeled 34° is on the top right. The angle labeled x is on the bottom left. These are alternate exterior angles? Or maybe not.

Actually, let’s use this: The angle adjacent to 146° on the top line is 34° (since 180 - 146 = 34). That 34° angle and the angle marked x are vertical angles? No — they are on different lines.

I think I made a mistake. Let me redraw mentally:

Top line: left to right — arrow, then angle 146°, then angle 34°, then arrow. So 146° and 34° are adjacent on the top line → sum to 180°, correct.

Transversal goes from top-right to bottom-left.

On the bottom line: the angle where the transversal meets — on the left side, it's labeled x. On the right side, it's unlabeled.

Now, the 34° angle (top right) and the angle on the bottom right (unlabeled) are corresponding angles → so bottom right angle = 34°.

Then, since x and that 34° angle are on a straight line (bottom line), x + 34° = 180° → x = 146°.

But wait — that can’t be right because 146° is already used. Alternatively, maybe x is vertically opposite to the 34° angle? No.

Another way: The angle marked x and the 146° angle are corresponding angles? Let’s see their positions.

Actually, standard rule: When two parallel lines are cut by a transversal, corresponding angles are equal. The 146° angle is on the top left. The angle on the bottom left (which is x) is in the same relative position → so they are corresponding angles! Therefore, x = 146°.

Yes! That makes sense. Because both are on the left side of the transversal and above/below the parallel lines respectively — but since the lines are parallel, corresponding angles are equal.

So for problem 1: x = 146°

Wait — but let me confirm with another method. The 34° angle is on the top right. Its corresponding angle on the bottom right would be 34°. Then, on the bottom line, the angles on either side of the transversal must add to 180°, so x + 34° = 180° → x = 146°. Same answer.

Good.

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Problem 2)
Two vertical parallel lines cut by a horizontal transversal. Angles given: 93° and 87° on the right side. Note: 93° + 87° = 180°, which is correct for a straight line.

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 be equal? But wait — actually, the 93° and x are on opposite sides of the transversal.

Actually, the 93° angle and the angle vertically opposite to x might be related.

Note: The 87° angle and x are corresponding angles? Let’s see: 87° is on the bottom right, x is on the top left — not corresponding.

Better: The angle adjacent to 93° on the right is 87°, which is fine.

Now, the angle marked x is on the top left. The angle directly across from it (vertically opposite) would be on the bottom right — which is 87°. Vertical angles are equal, so if x were vertically opposite to 87°, then x=87°. But is it?

Looking at the diagram: the transversal is horizontal. Left vertical line has angle x at the top. Right vertical line has 93° at the top and 87° at the bottom.

Actually, the 93° angle and the angle on the left at the top (x) are alternate interior angles? Or corresponding?

Standard: For two parallel lines cut by a transversal, alternate interior angles are equal.

Here, the 87° angle is on the bottom right. The angle on the top left (x) — are they alternate interior? Let’s define:

- Interior means between the two parallel lines.
- Alternate means on opposite sides of the transversal.

So, 87° is on the bottom right, between the lines. x is on the top left, also between the lines? If the transversal is horizontal, and lines are vertical, then "between" might not apply well.

Perhaps easier: The angle x and the 87° angle are corresponding angles if we consider direction.

Actually, notice that the 93° and 87° are supplementary, as expected.

The angle x is vertically opposite to the angle that is corresponding to 87°.

Let’s think differently: The angle adjacent to x on the left line (below it) should be equal to 93° because they are corresponding angles (both on the top side of the transversal, left and right lines).

If the angle below x on the left line is 93°, then since x and that angle are on a straight line (the left vertical line), x + 93° = 180° → x = 87°.

Yes! Because the left vertical line is straight, so angles on it add to 180°. And the angle below x corresponds to the 93° angle on the right (same side of transversal, both above the intersection? Wait.

Actually, the 93° angle is on the top right. The angle on the top left (x) — if the lines are parallel, then the consecutive interior angles should be supplementary? Or corresponding.

I recall: when two parallel lines are cut by a transversal, the consecutive interior angles are supplementary.

But here, perhaps simplest: the angle marked x and the 87° angle are vertical angles? No.

Let me assign: call the intersection points.

At the right intersection: top angle is 93°, bottom is 87°.

At the left intersection: top angle is x, bottom is y.

Since lines are parallel, the top angles should be equal if they are corresponding? But 93° and x — are they corresponding? Yes! Both are on the top side of the transversal and on the respective parallel lines. So corresponding angles are equal → x = 93°? But that contradicts earlier thought.

Wait — no: in standard definition, corresponding angles are in the same relative position. So if you go from top-left to bottom-right, etc.

Actually, for two vertical parallel lines cut by a horizontal transversal, the angles in the same quadrant are corresponding.

So top-left angle (x) and top-right angle (93°) are both above the transversal and on the left/right lines — so they are corresponding angles → thus x = 93°.

But then why is 87° given? 87° is the bottom-right angle, which should correspond to the bottom-left angle, say z, so z = 87°.

And indeed, on the left line, x + z = 93° + 87° = 180°, which is correct for a straight line.

So x = 93°.

But let me double-check with another pair. The 87° angle and the angle below x (z) are corresponding, so z = 87°, and x = 180° - z = 93°.

Yes.

So problem 2: x = 93°

Wait — but in the diagram, is x the top-left or bottom-left? The problem says "x =" and in figure 2, it's shown on the left side, and from the context, likely the top one. But let's assume based on standard labeling.

Actually, looking back at the user's image description, in figure 2, it shows two vertical arrows (parallel lines), horizontal transversal, with 93° and 87° on the right, and x on the left. Typically, x is placed at the top-left.

And since corresponding angles: top-left and top-right should be equal if the lines are parallel? No — that's not right.

I think I have a confusion.

Let me clarify with a standard example.

Suppose two parallel lines, cut by a transversal. Corresponding angles are like: both upper-left, or both upper-right, etc.

In this case, for vertical parallel lines and horizontal transversal:

- The angle at top-left of left line and top-left of right line — but the right line's top-left is actually the 93° angle? No.

When we say "position", for the right line, the angle above the transversal and to the left of the line is 93°? This is messy.

Better to use the fact that alternate interior angles are equal.

The 87° angle is on the bottom right. The alternate interior angle would be on the top left — which is x. Are they alternate interior?

Interior: between the two parallel lines. Since the lines are vertical, "between" is the region between them. The transversal is horizontal, so the angles inside the space between the lines are the ones facing each other.

So, the 87° angle is on the bottom right, which is between the lines if we consider the area between the vertical lines. Similarly, the angle on the top left (x) is also between the lines. And they are on opposite sides of the transversal (one below, one above? No, both are on the same side relative to the transversal?).

Actually, for two vertical lines, the "interior" is the strip between them. The transversal crosses them. The angle at the bottom-right intersection, below the transversal, is 87°. The angle at the top-left intersection, above the transversal, is x. These are not alternate interior; they are on different sides.

Alternate interior angles would be: for example, the angle below the transversal on the right line (87°) and the angle above the transversal on the left line (x) — but only if they are on opposite sides of the transversal, which they are not; both are on the "inside" but same side? I'm confusing myself.

Let's use a different strategy: the sum of angles around a point is 360°, but that might not help.

Notice that the 93° and 87° are adjacent on the right line, summing to 180°, good.

On the left line, the two angles must also sum to 180°. Let’s call the bottom-left angle y. Then x + y = 180°.

Now, the 93° angle (top-right) and the y angle (bottom-left) are alternate exterior angles? Or what.

Actually, the 93° angle and the y angle are corresponding if we consider the direction.

I recall that in such a setup, the angles that are "across" are equal if they are vertical, but here it's different lines.

Another idea: the angle x and the 87° angle are supplementary because they are consecutive interior angles? Let's calculate.

Assume that the 87° angle and the angle adjacent to x on the bottom are corresponding, so that angle is 87°. Then on the left line, x + 87° = 180° → x = 93°.

Same as before.

Or, the 93° angle and x are vertically opposite to something.

I think I need to accept that x = 93° is correct, as per corresponding angles if we consider the top angles.

But let's look at problem 5 or others for pattern.

Perhaps in figure 2, the x is meant to be the angle that is corresponding to the 87° angle.

Let's read the diagram description: "2) [diagram] with 93° and 87° on the right, x on the left."

In many textbooks, for two parallel lines cut by a transversal, if you have an angle on one side, the corresponding angle on the other line is equal.

So, the 87° angle is on the bottom right. The corresponding angle on the bottom left would be equal to 87°. But x is on the top left, so not that.

The 93° is on the top right, so corresponding angle on the top left is x, so x = 93°.

Yes, I think that's it.

So problem 2: x = 93°

But let's move on and come back if needed.

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Problem 3)
Two horizontal parallel lines cut by a transversal. Angles given: 75° and 106° on the top line. Note: 75° + 106° = 181° — that can't be right; must be a typo or misread.

75° and 106° are adjacent on the top line? 75 + 106 = 181, which is not 180, so impossible. Perhaps they are not adjacent.

Looking at the diagram: probably 75° and 106° are on the same side, but not adjacent. Or perhaps 106° is the larger angle.

Actually, in the top line, the transversal creates two angles: one is 75°, the other is 106°, but 75 + 106 = 181 > 180, so error.

Perhaps 106° is the reflex or something, but unlikely.

Another possibility: the 75° and 106° are on different parts. Let's assume that on the top line, the angle on the left is 75°, on the right is 106°, but that doesn't make sense for a straight line.

Unless the 106° is not on the top line alone. Perhaps the 106° is the angle between the transversal and the top line on the right side, and 75° on the left side, but then they should sum to 180 if they are adjacent.

75 + 106 = 181, close to 180, perhaps it's 74° or 105°, but we have to work with given numbers.

Perhaps the 75° and 106° are not both on the top line; let's read the diagram.

In figure 3: "75° 106°" on the top, and x on the bottom.

Probably, the 75° and 106° are the two angles formed by the transversal with the top line, but they must sum to 180°, so 75 + 106 = 181 is impossible. Likely a typo, and it's 74° and 106°, or 75° and 105°.

Perhaps 106° is the angle including something else.

Another interpretation: the 75° is one angle, and 106° is the adjacent angle on the other side, but still.

Let's calculate what it should be. If the transversal cuts the top line, the two adjacent angles sum to 180°. So if one is 75°, the other should be 105°. Probably it's 105°, and it's written as 106° by mistake, or vice versa.

Perhaps the 106° is the angle for the bottom or something.

Let's look at the position. In many diagrams, they show the acute and obtuse angles.

Assume that on the top line, the angle on the left is 75°, so the angle on the right is 180° - 75° = 105°. But it's labeled 106°, so perhaps it's 106°, and 75° is wrong.

75 + 106 = 181, so difference of 1°, likely a rounding or typo, but for accuracy, perhaps we should use the given numbers as is, but that doesn't work.

Another idea: perhaps the 75° and 106° are not both on the top line; maybe 75° is on the top, 106° is on the bottom or something.

The diagram says: "75° 106°" near the top intersection, and x at the bottom intersection.

Probably, the 75° and 106° are the two angles at the top intersection, but they must sum to 180°, so perhaps it's 74° and 106°, or 75° and 105°.

Let's assume it's 75° and 105°, and 106° is a typo. Or perhaps 106° is the measure of the angle that is vertical to something.

Let's think differently. The angle x is at the bottom intersection. The corresponding angle to x on the top line would be the angle in the same position.

For example, if x is on the bottom left, then the corresponding angle on the top left is 75°, so x = 75°.

But then what is 106° for? Perhaps 106° is the adjacent angle on the top line, so 180° - 75° = 105°, close to 106°, so likely x = 75°.

Perhaps the 106° is the angle that is supplementary to the corresponding angle.

Let's calculate the actual value. Suppose the top-left angle is A, top-right is B, with A + B = 180°.

Given A = 75°, B = 106°, but 75+106=181, so inconsistency.

Perhaps the 75° and 106° are not both at the top; maybe 75° is at the top, 106° is at the bottom, but the diagram shows them together.

Another possibility: the 106° is the angle between the transversal and the top line on the right, and 75° on the left, but then for the straight line, it should be 180, so perhaps the 106° includes the 75° or something.

I think there might be a mistake in my assumption. Let's look for similar problems.

Perhaps in figure 3, the 75° and 106° are on the same side, but 106° is the larger angle, and 75° is part of it, but that doesn't make sense.

Let's ignore the sum and use correspondence.

Typically, in such diagrams, the angle marked x corresponds to one of the given angles.

Suppose that the 75° angle and x are corresponding angles. Then x = 75°.

Or, the 106° angle and x are corresponding, so x = 106°.

But which one?

Notice that 75° and 106° are adjacent, so they are on a straight line, so their sum should be 180°, but 75+106=181, so perhaps it's 74° and 106°, or 75° and 105°.

Let's assume it's 75° and 105°, and proceed with x = 75° if corresponding.

Perhaps the 106° is the angle that is vertical to the angle corresponding to x.

Let's calculate the angle that is supplementary.

Another approach: the angle x and the 106° angle might be alternate interior or something.

Let's assume that the 75° angle is on the top left, so its corresponding angle on the bottom left is x, so x = 75°.

Then the 106° might be a distractor or for another purpose, but in the diagram, it's given, so probably not.

Perhaps the 106° is the measure of the angle on the top right, and 75° on the top left, but 75+106=181, so error.

For the sake of progress, let's take x = 75°, as it's likely the corresponding angle.

Or perhaps x = 106°.

Let's see the position. In many cases, the angle x is corresponding to the acute angle or something.

Perhaps the 75° and 106° are not both at the top; let's read the user's input: "3) [diagram] with 75° 106°" and x below.

Upon second thought, in some diagrams, they show the angle between the lines, but here it's specified as angles at the intersection.

I recall that in such problems, if two angles are given at one intersection, they are adjacent, so sum to 180°. Here 75+106=181, so likely a typo, and it's 74° and 106°, or 75° and 105°.

Let's assume it's 75° and 105°, and the 106° is a mistake, or vice versa.

Perhaps the 106° is the angle for the bottom, but the diagram shows it at the top.

Another idea: perhaps the 75° is the angle on the top left, and 106° is the angle on the bottom right or something, but the diagram places them together.

To resolve, let's look at the answer choices or standard values.

Perhaps the 75° and 106° are the measures, and we need to find which one corresponds to x.

Let's suppose that the angle x is corresponding to the 75° angle, so x = 75°.

Or, if x is corresponding to the 106° angle, x = 106°.

But 106° is obtuse, 75° acute.

In the bottom, x is likely acute or obtuse depending.

Perhaps from the diagram, x is on the same side as the 75° angle.

I think for now, I'll assume that the 75° angle and x are corresponding, so x = 75°.

But let's check with calculation. If the top-left angle is 75°, then the bottom-left angle (x) is corresponding, so x = 75°.

The 106° might be the top-right angle, which should be 180° - 75° = 105°, so perhaps it's 105°, and 106° is a typo. We'll go with x = 75°.

So problem 3: x = 75°

But to be accurate, let's say if the given angles are 75° and 106°, and they are adjacent, then their sum is 181°, which is impossible, so perhaps in the context, we take the corresponding angle.

Perhaps the 106° is the angle that is vertical to the angle supplementary to x.

Let's calculate the actual corresponding angle.

Suppose that the angle adjacent to 75° on the top line is 180° - 75° = 105°, but it's labeled 106°, so close.

Perhaps for this problem, x = 106°, if it's corresponding to the 106° angle.

I think I need to move on and come back.

Let's do problem 4.

Problem 4)
Two vertical parallel lines cut by a transversal. Angles given: 69° and 111° on the right side. 69° + 111° = 180°, good.

Angle x is on the left side, at the top.

Similar to problem 2.

The 69° angle is on the top right, 111° on the bottom right.

Corresponding angle to 69° on the left side (top left) is x, so x = 69°.

Because both are on the top side of the transversal, and on the respective parallel lines.

So x = 69°.

Confirm: on the left line, the bottom-left angle would correspond to 111°, so 111°, and x + 111° = 180°, so x = 69°, yes.

So problem 4: x = 69°

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Problem 5)
Two horizontal parallel lines cut by a transversal. Angles given: 150° and 30° on the bottom line. 150° + 30° = 180°, good.

Angle x is on the top line, at the left.

The 30° angle is on the bottom right. The corresponding angle on the top right would be 30°.

Then, on the top line, the angle adjacent to x on the right is 30°, so x + 30° = 180° → x = 150°.

The 150° is given on the bottom left, which should correspond to the top left angle x, so x = 150°.

Yes, because both are on the left side of the transversal, and above/below, but since lines are parallel, corresponding angles are equal.

So x = 150°.

Problem 5: x = 150°

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Problem 6)
Two vertical parallel lines cut by a transversal. Angles given: 128° and 52° on the right side. 128° + 52° = 180°, good.

Angle x is on the left side, at the top.

The 128° angle is on the top right, 52° on the bottom right.

Corresponding angle to 128° on the left side (top left) is x, so x = 128°.

On the left line, the bottom-left angle would be 52°, and 128° + 52° = 180°, good.

So problem 6: x = 128°

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Problem 7)
Two horizontal parallel lines cut by a transversal. Angles given: 131° and 49° on the bottom line. 131° + 49° = 180°, good.

Angle x is on the top line, at the left.

The 49° angle is on the bottom right. Corresponding angle on the top right is 49°.

Then on the top line, x + 49° = 180° → x = 131°.

The 131° is on the bottom left, which corresponds to the top left angle x, so x = 131°.

Yes.

Problem 7: x = 131°

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Problem 8)
Two vertical parallel lines cut by a transversal. Angles given: 103° and 77° on the right side. 103° + 77° = 180°, good.

Angle x is on the left side, at the top.

Corresponding angle to 103° (top right) on the left side (top left) is x, so x = 103°.

On the left line, bottom-left angle corresponds to 77°, so 77°, and 103° + 77° = 180°, good.

Problem 8: x = 103°

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Problem 9)
Two horizontal parallel lines cut by a transversal. Angles given: 114° and 66° on the bottom line. 114° + 66° = 180°, good.

Angle x is on the top line, at the right.

The 66° angle is on the bottom right. Corresponding angle on the top right is x, so x = 66°.

The 114° is on the bottom left, which corresponds to the top left angle, not x.

So x = 66°.

Problem 9: x = 66°

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Now, back to problem 3. We have issue with 75° and 106° summing to 181°.

Perhaps in the diagram, the 75° and 106° are not both at the top intersection; maybe 75° is at the top, and 106° is at the bottom, but the diagram shows them together.

Perhaps the 106° is the angle for the bottom, but labeled near the top.

Another possibility: the 75° is the angle between the transversal and the top line on the left, and 106° is the angle between the transversal and the bottom line on the right or something.

Let's assume that the angle x is corresponding to the 75° angle, so x = 75°.

Or, perhaps the 106° is the measure of the angle that is vertical to the angle supplementary to x.

Let's calculate what x should be if the lines are parallel.

Suppose that the top-left angle is A, then bottom-left angle x = A (corresponding).

Top-right angle B = 180° - A.

Bottom-right angle C = B = 180° - A (corresponding).

In the diagram, they give 75° and 106° at the top, so perhaps A = 75°, B = 106°, but 75+106=181, so not possible.

Perhaps the 75° is A, and 106° is C or something.

Another idea: perhaps the 75° and 106° are the measures of the angles at the two intersections, but not specified.

Let's look for the most reasonable answer.

Perhaps the 106° is the angle on the top right, and 75° is on the bottom left or something.

I recall that in some diagrams, they show the angle and its supplement.

Let's assume that the 75° angle and x are alternate interior or something.

Perhaps x = 106°, if it's corresponding to the 106° angle.

But let's notice that 180° - 75° = 105°, and 106° is close, so perhaps it's 105°, and x = 75°.

Or, if the 106° is given, and it's the angle on the top right, then the corresponding angle on the bottom right is 106°, but x is on the bottom left, so not.

Let's suppose that the angle x is vertically opposite to the 75° angle or something.

I think for consistency, in all other problems, x is equal to the angle in the corresponding position.

In problem 3, if we assume that the 75° is on the top left, then x on the bottom left is corresponding, so x = 75°.

The 106° might be a red herring or for another purpose, but likely it's the top-right angle, which should be 105°, so we'll go with x = 75°.

Perhaps the 106° is the measure of the angle that is supplementary to the corresponding angle.

Let's calculate: if x is the bottom-left angle, then the top-left angle is also x (corresponding).

Then the top-right angle is 180° - x.

If they give 75° and 106°, perhaps 75° is the top-left, so x = 75°, and 106° is approximately 105°, so ok.

Or, if 106° is the top-right, then 180° - x = 106°, so x = 74°, but 75° is given, so not.

Perhaps the 75° is the bottom-right or something.

I think the intended answer is x = 75°, as it's likely the corresponding angle.

So I'll go with that.

Problem 3: x = 75°

But to be precise, let's box the answers.

Also, for problem 2, we had x = 93°, but let's confirm with the pattern.

In problem 2, with 93° and 87°, x = 93°.

In problem 4, 69° and 111°, x = 69°.

In problem 6, 128° and 52°, x = 128°.

In problem 8, 103° and 77°, x = 103°.

So in all cases, x is equal to the top-right angle or the first given angle.

In problem 3, the first given is 75°, so x = 75°.

Similarly, in problem 1, we had x = 146°, which is the first angle given.

In problem 1, 146° and 34°, x = 146°.

In problem 5, 150° and 30°, x = 150°.

In problem 7, 131° and 49°, x = 131°.

In problem 9, 114° and 66°, but x = 66°, which is the second angle.

In problem 9, x is on the top right, and 66° is on the bottom right, so corresponding, so x = 66°.

In problem 3, if x is on the bottom left, and 75°