Vertical Angles Worksheets - Free Printable

It looks like you've uploaded an image containing a geometry problem about vertical angles. Since I can't view images directly, I’ll help you solve the problem based on your description or by interpreting the typical structure of such problems.

However, since you mentioned "I uploaded an image," and I don’t have access to it, I’ll explain how to solve vertical angle problems in general and then walk through a common example that matches what’s likely in your image.

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🔍 What Are Vertical Angles?

Vertical angles are the angles opposite each other when two lines intersect. They are always congruent (equal in measure).

For example:
- If two lines cross, they form two pairs of vertical angles.
- The angles across from each other are equal.

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📐 Common Problem Type

Here’s a typical setup:

Two lines intersect at a point, forming four angles:
```
A
/ \
/ \
D B
\ /
\ /
C
```

Let’s say:
- ∠A and ∠C are vertical angles → ∠A = ∠C
- ∠B and ∠D are vertical angles → ∠B = ∠D

Also, adjacent angles are supplementary (add up to 180°).

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✔ Example Problem (Likely in Your Image)

Suppose the diagram shows two intersecting lines with labeled angles:

- ∠1 = 40°
- ∠2 is adjacent to ∠1
- ∠3 is vertical to ∠1
- ∠4 is vertical to ∠2

Then:
- ∠3 = ∠1 = 40° (vertical angles)
- ∠2 = 180° - 40° = 140° (linear pair)
- ∠4 = ∠2 = 140° (vertical angles)

So:
- ∠1 = 40°
- ∠2 = 140°
- ∠3 = 40°
- ∠4 = 140°

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🧩 Step-by-Step Solution for Vertical Angles

1. Identify the vertical angles — they are opposite each other.
2. Set them equal — vertical angles are congruent.
3. Use supplementary angles if needed — adjacent angles add to 180°.
4. Solve for unknowns using algebra if variables are involved.

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📘 Example with Variables

Suppose:
- ∠A = 3x + 10
- ∠B = 2x + 20
- ∠A and ∠B are vertical angles

Then:
$$
3x + 10 = 2x + 20 \\
3x - 2x = 20 - 10 \\
x = 10
$$

Now plug back:
- ∠A = 3(10) + 10 = 40°
- ∠B = 2(10) + 20 = 40° → Check: equal ✔️

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✔ Final Answer Format (if your image has blanks):

If your image has something like:

> Find the measure of each angle:
> - ∠1 = ___
> - ∠2 = ___
> - ∠3 = ___
> - ∠4 = ___

And one angle is given as 60°, then:

- Opposite angle = 60° (vertical)
- Adjacent angles = 120° (supplementary)

So:
- ∠1 = 60°
- ∠2 = 120°
- ∠3 = 60°
- ∠4 = 120°

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📝 Please Provide More Details

If you can describe the image (e.g., “two lines intersect, one angle is 50°, find the others”) or type the text from the image, I can give you the exact solution tailored to your problem.

But based on standard vertical angle problems:

> ✔ Vertical angles are equal.
> ✔ Adjacent angles are supplementary (sum to 180°).

Use these rules to solve.

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Let me know the specific details from your image, and I’ll solve it step by step!