Free Printable & Interactive Vertical Angles Worksheets - Free Printable

To find the vertical angle measurements, we need to use the Vertical Angles Theorem. This theorem states that when two lines intersect, the angles opposite each other (called vertical angles) are equal in measure.

Let’s go through each diagram one by one and identify the vertical angle for the given measured angle.

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Diagram 1 (top left):
Given angles: 67° and 113°
These are adjacent angles on a straight line — they add up to 180°, which checks out (67 + 113 = 180).
The vertical angle to 67° is the angle directly opposite it — which must also be 67°.
The vertical angle to 113° is the angle directly opposite it — which must also be 113°.
But since the problem says “find the vertical angle measurements for the measured angles,” and both are already labeled, we just note their opposites are the same. However, looking at the diagram, only one angle per pair is labeled with its measure — actually, wait — in this diagram, *both* adjacent angles are labeled. So perhaps the task is to label the *other two* angles? But no — vertical angles are across from each other.

Actually, re-reading the instruction: “Find the vertical angle measurements for the measured angles.” That means: for each angle that has a number written next to it, what is the measure of its vertical counterpart?

In Diagram 1:
- The 67° angle’s vertical partner is the angle opposite it → also 67°
- The 113° angle’s vertical partner is the angle opposite it → also 113°

But those opposite angles aren’t labeled — so we’re being asked to state what they are.

Wait — let me look again at all diagrams. In some, only one angle is labeled; in others, two adjacent ones are labeled. The key is: vertical angles are always equal. So if an angle is labeled X°, its vertical angle is also X°.

Let’s process each diagram carefully:

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Diagram 1 (top left):
Angles shown: 67° and 113° (adjacent, forming a linear pair)
→ Vertical angle to 67° = 67°
→ Vertical angle to 113° = 113°
*(So the unlabeled angles opposite them are 67° and 113° respectively)*

But the question says “for the measured angles” — meaning, take each labeled angle and give its vertical angle measure.

So for 67° → vertical angle is 67°
For 113° → vertical angle is 113°

Same logic applies everywhere.

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Diagram 2 (top right):
Labeled angles: 15° and 165° (again, adjacent, sum to 180°)
→ Vertical angle to 15° = 15°
→ Vertical angle to 165° = 165°

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Diagram 3 (middle left):
Labeled angles: 26° and 154°
→ Vertical angle to 26° = 26°
→ Vertical angle to 154° = 154°

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Diagram 4 (middle right):
Labeled angles: 142° and 38°
→ Vertical angle to 142° = 142°
→ Vertical angle to 38° = 38°

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Diagram 5 (bottom left):
Labeled angles: 112° and 68°
→ Vertical angle to 112° = 112°
→ Vertical angle to 68° = 68°

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Diagram 6 (bottom right):
Only one angle labeled: 111°
Its vertical angle (opposite it) is also 111°

Note: The adjacent angle would be 180° - 111° = 69°, but that’s not asked. We only care about the vertical angle to the measured angle.

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So, summarizing for each diagram, the vertical angle(s) corresponding to the labeled angle(s):

We can list them as pairs or just state the vertical angle measures.

Since the worksheet likely expects you to write the measure of the vertical angle for each labeled angle, here’s how to present it:

For each labeled angle, its vertical angle has the same measure.

Thus:

- For 67° → vertical angle = 67°
- For 113° → vertical angle = 113°
- For 15° → vertical angle = 15°
- For 165° → vertical angle = 165°
- For 26° → vertical angle = 26°
- For 154° → vertical angle = 154°
- For 142° → vertical angle = 142°
- For 38° → vertical angle = 38°
- For 112° → vertical angle = 112°
- For 68° → vertical angle = 68°
- For 111° → vertical angle = 111°

But since the diagrams are separate, maybe we should group by diagram.

Alternatively, perhaps the worksheet wants you to fill in the blank angles — but the instruction says “find the vertical angle measurements for the measured angles,” which implies: given a measured angle, what is its vertical angle’s measure? Answer: same number.

So final answer should list the vertical angle measures corresponding to each labeled angle.

But to match typical worksheet format, let’s assume we’re to provide the measure of the vertical angle for each labeled angle in order.

Looking at the layout:

There are 6 diagrams. Let’s number them 1 to 6 from top-left to bottom-right.

Diagram 1: labeled 67° and 113° → vertical angles: 67° and 113°
Diagram 2: labeled 15° and 165° → vertical angles: 15° and 165°
Diagram 3: labeled 26° and 154° → vertical angles: 26° and 154°
Diagram 4: labeled 142° and 38° → vertical angles: 142° and 38°
Diagram 5: labeled 112° and 68° → vertical angles: 112° and 68°
Diagram 6: labeled 111° → vertical angle: 111°

But since the problem says “the vertical angle measurements for the measured angles”, and there are multiple measured angles per diagram in most cases, we should report all.

However, in many such worksheets, even if two angles are labeled, they might expect you to recognize that vertical angles are equal, so the answer is simply repeating the given measures for their opposites.

Perhaps the expected answer is to list the vertical angle for each labeled angle, in the order they appear.

To avoid confusion, I’ll list the vertical angle measure for each labeled angle, going row by row, left to right.

Final Answer will be a list of the vertical angle measures corresponding to each labeled angle in the diagrams.

But let’s double-check Diagram 6: only 111° is labeled. Its vertical angle is 111°. The adjacent angle is 69°, but that’s not vertical — so we don’t report that.

All good.

Now, compiling the final answer:

Since the problem doesn’t specify formatting, but typically in such sheets, you’d write the answer next to each diagram or in a list.

I think the cleanest way is to state:

The vertical angle for each measured angle is equal to the measured angle itself.

So:

- 67° → 67°
- 113° → 113°
- 15° → 15°
- 165° → 165°
- 26° → 26°
- 154° → 154°
- 142° → 142°
- 38° → 38°
- 112° → 112°
- 68° → 68°
- 111° → 111°

But to match the diagram count, perhaps group per diagram.

Alternatively, since the user may expect a simple list, I'll provide the vertical angle measures in the order of the labeled angles as they appear in the diagrams from top to bottom, left to right.

Order of labeled angles in diagrams:

1. Top-left: 67°, then 113°
2. Top-right: 15°, then 165°
3. Middle-left: 26°, then 154°
4. Middle-right: 142°, then 38°
5. Bottom-left: 112°, then 68°
6. Bottom-right: 111°

So the vertical angles are:

67°, 113°, 15°, 165°, 26°, 154°, 142°, 38°, 112°, 68°, 111°

But that seems redundant because it's the same as the given angles.

Yes — that’s the point! Vertical angles are equal, so the answer is identical to the given measures.

Therefore, the final answer is simply listing those values as the vertical angle measures.

I think that’s correct.

Final Answer:
67°, 113°, 15°, 165°, 26°, 154°, 142°, 38°, 112°, 68°, 111°