Naming Angles Worksheets - Free Printable

Since I can't view or access images directly, I can't see the specific angles in your uploaded worksheet. However, I can help you solve "Naming Angles with a Common Vertex" problems based on standard geometry principles.

Let me walk you through how to approach this type of problem and then guide you through each question assuming typical configurations (which are common in such worksheets).

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🔷 How to Name Angles with a Common Vertex

When multiple angles share the same vertex (the point where two rays meet), we name them using three points:
- The first point is on one ray.
- The second point is the vertex (middle).
- The third point is on the other ray.

For example:
If angle is formed by rays from point A to B and A to C, the angle is named ∠BAC or ∠CAB — always putting the vertex in the middle.

We use three letters to avoid confusion when there are multiple angles at the same vertex.

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Now, let’s go through the six problems as they typically appear in such worksheets.

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✔ Problem 1:

```
A
/ \
/ \
/ \
B-------C
```

Assuming:
- Point B is the vertex.
- Rays go from B to A and B to C.

There's only one angle here: ∠ABC

But if there are more rays (like an angle split into two), we’d have multiple angles.

Wait — looking at your description, it says "angles with a common vertex", so likely each diagram has multiple rays from one point.

Let’s assume each figure shows three or more rays emanating from a single point.

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📌 General Approach for Each Diagram:

1. Identify the common vertex (usually labeled).
2. List all possible angles formed by pairs of rays.
3. Use three-letter notation with the vertex in the middle.
4. Be careful not to miss any combinations.

---

Let’s now assume the diagrams look like these common examples:

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Problem 1:

```
A
/
/
/
/
B-----C
```

But wait — that's just one angle. Let's suppose instead:

#### 🔹 Diagram 1: Three rays from point D — DA, DB, DC
So angles are:
- ∠ADB (between DA and DB)
- ∠BDC (between DB and DC)
- ∠ADC (between DA and DC)

✔ Answer: ∠ADB, ∠BDC, ∠ADC

---

Problem 2:

Similar to above but different labels.

Suppose rays from point E: EA, EB, EC

Then angles:
- ∠AEB
- ∠BEC
- ∠AEC

✔ Answer: ∠AEB, ∠BEC, ∠AEC

---

Problem 3:

```
D
|
|
|
|
C---E---F
```

Vertex at E? Or at C?

Wait — if it's a right angle at E, with rays going up and right, and another ray diagonal?

Let’s assume:
- Vertex at E
- Rays: ED (up), EF (right), and EC (diagonal down-left)

Then possible angles:
- ∠DEF (between ED and EF)
- ∠DEC (between ED and EC)
- ∠CEF (between EC and EF)

But maybe it's simpler: two rays forming a right angle, and a third ray splitting it.

But without seeing image, let’s assume:

#### 🔹 Diagram 3: Right angle at E, with ray EC inside it

Rays: EA (left), EB (up), EC (diagonal), ED (right)

But usually, it's something like:
- Ray ED upward
- Ray EF to the right
- Ray EG diagonally between

Then angles:
- ∠DEF
- ∠FEG
- ∠DEG

So answer: ∠DEF, ∠FEG, ∠DEG

---

Problem 4:

Likely similar — three rays from one point.

Suppose vertex at H, rays HA, HB, HC

Then:
- ∠AHB
- ∠BHC
- ∠AHC

✔ Answer: ∠AHB, ∠BHC, ∠AHC

---

Problem 5:

Maybe a triangle-like shape with shared vertex H.

Suppose rays from H: HA, HB, HC

Then again:
- ∠AHD (if D is label)
Wait — better to assume:

If rays are HA, HB, HC from point H, then:
- ∠AHB
- ∠BHC
- ∠AHC

✔ Answer: ∠AHB, ∠BHC, ∠AHC

---

Problem 6:

Possibly a star-like shape with four rays from a central point.

Say vertex at O, rays OA, OB, OC, OD

Then angles:
- ∠AOB
- ∠BOC
- ∠COD
- ∠DOA
- ∠AOC (skip over)
- ∠BOD

But typically, we list adjacent angles only unless specified otherwise.

Usually, the worksheet wants all distinct angles formed by adjacent rays.

So if rays are in order: OA, OB, OC, OD around point O,

Then angles:
- ∠AOB
- ∠BOC
- ∠COD
- ∠DOA

And possibly:
- ∠AOC (spanning two)
- ∠BOD
- ∠AOD

But again, depends on instruction.

Typically, they want all possible angles with the common vertex.

So for 4 rays, number of angles = C(4,2) = 6 angles.

But often, only adjacent ones are listed.

---

✔ Final Strategy:

To solve your worksheet:

For each diagram:
1. Find the common vertex (labeled point where all rays meet).
2. Label the rays going out from that point.
3. For every pair of rays, form an angle using three-letter notation (ray1-vertex-ray2).
4. Write all such angles.

---

🧩 Example Answer Format:

Problem 1:
Angles: ∠ADB, ∠BDC, ∠ADC

Problem 2:
Angles: ∠AEB, ∠BEC, ∠AEC

Problem 3:
Angles: ∠DEF, ∠FEG, ∠DEG

Problem 4:
Angles: ∠AFB, ∠BFC, ∠AFC

Problem 5:
Angles: ∠AHC, ∠CHB, ∠AHB

Problem 6:
Angles: ∠AOB, ∠BOC, ∠COD, ∠DOA, ∠AOC, ∠BOD

---

⚠️ But since I don’t have the actual image, please describe each diagram, or provide the labels of the points in each figure, and I’ll give you the exact answers.

Alternatively, if you can describe what each diagram looks like (e.g., “Three rays from point D: DA, DB, DC”), I can fill in the blanks correctly.

Would you like to do that?