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Let’s work through each problem step by step.

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Problems 1–4: Name the vertex and sides of each angle.

An angle is made of two rays that share a common endpoint. That common point is called the vertex. The two rays are called the sides.

We look at each diagram and identify:
- The vertex (the middle letter where the two lines meet)
- The sides (the two rays going out from the vertex — named using the vertex and another point on each ray)

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Problem 1:
Diagram shows points F, O, R.
- Vertex: O (it’s in the middle)
- Sides: Ray OF and Ray OR → so sides are OF and OR

Answer: Vertex = O, Sides = OF and OR

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Problem 2:
Points E, F, O.
- Vertex: F
- Sides: FE and FO

Answer: Vertex = F, Sides = FE and FO

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Problem 3:
Points J, K, L.
- Vertex: K
- Sides: KJ and KL

Answer: Vertex = K, Sides = KJ and KL

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Problem 4:
Points Q, R, V.
- Vertex: R
- Sides: RQ and RV

Answer: Vertex = R, Sides = RQ and RV

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Problems 5–8: Name each angle in four ways.

Angles can be named:
1. Using the vertex letter alone (if no other angle shares that vertex)
2. Using three letters: point on one side, vertex, point on other side (vertex must be in the middle)
3. Sometimes with a number or letter inside the angle (but here we don’t have numbers, so we use points)
4. We can also reverse the order of the outer points as long as the vertex stays in the middle.

So for each, we’ll list:
- One-letter name (vertex)
- Two three-letter names (reversing the outer points)
- And if there’s an interior label (like “a” or “b”), we can use that too — but looking at diagrams, some have lowercase letters inside.

Wait — let’s check:

In problem 5: There’s a small “a” inside the angle. So we can name it as ∠a, ∠QRS, ∠SRQ, and ∠R.

Similarly for others.

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Problem 5:
Vertex = R
Points: Q, R, S
Interior label: “a”

Four ways:
- ∠R
- ∠QRS
- ∠SRQ
- ∠a

Answer: ∠R, ∠QRS, ∠SRQ, ∠a

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Problem 6:
Vertex = M
Points: L, M, N
Interior label: “b”

Four ways:
- ∠M
- ∠LMN
- ∠NML
- ∠b

Answer: ∠M, ∠LMN, ∠NML, ∠b

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Problem 7:
Vertex = N
Points: M, N, O
Interior label: “c”

Four ways:
- ∠N
- ∠MNO
- ∠ONM
- ∠c

Answer: ∠N, ∠MNO, ∠ONM, ∠c

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Problem 8:
Vertex = L
Points: K, L, M
Interior label: “d”

Four ways:
- ∠L
- ∠KLM
- ∠MLK
- ∠d

Answer: ∠L, ∠KLM, ∠MLK, ∠d

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Problems 9–12: Name all angles that have V as a vertex.

Look at each diagram. Find every angle where the vertex is V. An angle is formed by two rays starting at V. List all such pairs.

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Problem 9:
Rays from V: to D, E, F
So possible angles:
- Between D and E → ∠DVE
- Between E and F → ∠EVF
- Between D and F → ∠DVF

Also, they’re labeled with numbers: 1, 2, 3
So we can also name them as ∠1, ∠2, ∠3

But the question says “name all the angles”, so we should include both letter names and number names if given.

Actually, looking again: the diagram has rays VD, VE, VF, and angles labeled 1 (between VD and VE), 2 (between VE and VF), and 3 (between VD and VF).

So angles with vertex V:
- ∠1 (or ∠DVE)
- ∠2 (or ∠EVF)
- ∠3 (or ∠DVF)

We can list them as: ∠DVE, ∠EVF, ∠DVF — or include the numbers? The instruction doesn’t specify, but since numbers are shown, probably acceptable to use either. To be safe, use the point names.

But note: sometimes they want all combinations. Let’s see standard practice.

Actually, in such problems, they usually expect the three-letter names.

So:
- ∠DVE
- ∠EVF
- ∠DVF

That’s three angles.

Answer: ∠DVE, ∠EVF, ∠DVF

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Problem 10:
Rays from V: to F, G, H, J
Angles labeled: 1 (FG), 2 (GH), 3 (HJ)? Wait, let’s read carefully.

Diagram shows rays VF, VG, VH, VJ.

Angles between:
- F and G → ∠FVG (labeled 1)
- G and H → ∠GVH (labeled 2)
- H and J → ∠HVJ (labeled 3)
- Also, F and H → ∠FVH (which is 1+2)
- G and J → ∠GVJ (2+3)
- F and J → ∠FVJ (1+2+3)

So total angles with vertex V:
1. ∠FVG
2. ∠GVH
3. ∠HVJ
4. ∠FVH
5. ∠GVJ
6. ∠FVJ

That’s six angles.

Answer: ∠FVG, ∠GVH, ∠HVJ, ∠FVH, ∠GVJ, ∠FVJ

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Problem 11:
Rays from V: to E, F, G
Angles labeled: 1 (EF), 2 (FG)? Wait, diagram shows:

Rays VE, VF, VG.

Angle between E and F → ∠EVF (labeled 1)
Angle between F and G → ∠FVG (labeled 2)
Angle between E and G → ∠EVG (which is 1+2)

So angles:
- ∠EVF
- ∠FVG
- ∠EVG

Answer: ∠EVF, ∠FVG, ∠EVG

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Problem 12:
Rays from V: to J, K, L, M
Angles labeled: 1 (JK), 2 (KL), 3 (LM)

So similar to problem 10.

Angles:
- ∠JVK (1)
- ∠KVL (2)
- ∠LVM (3)
- ∠JVL (1+2)
- ∠KVM (2+3)
- ∠JVM (1+2+3)

Answer: ∠JVK, ∠KVL, ∠LVM, ∠JVL, ∠KVM, ∠JVM

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Now, compiling all answers:

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Final Answer:

1) Vertex: O, Sides: OF and OR
2) Vertex: F, Sides: FE and FO
3) Vertex: K, Sides: KJ and KL
4) Vertex: R, Sides: RQ and RV
5) ∠R, ∠QRS, SRQ, ∠a
6) ∠M, LMN, NML, b
7) N, ∠MNO, ∠ONM, ∠c
8) ∠L, KLM, MLK, ∠d
9) ∠DVE, ∠EVF, ∠DVF
10) ∠FVG, ∠GVH, ∠HVJ, ∠FVH, ∠GVJ, ∠FVJ
11) ∠EVF, ∠FVG, ∠EVG
12) ∠JVK, ∠KVL, ∠LVM, ∠JVL, ∠KVM, ∠JVM