Geometry worksheet for naming angles and identifying vertices and sides.

Based on the analysis of the worksheet, here are the solutions for each problem:

Section 1: Name the vertex and sides of each angle (Problems 1-4)

Problem 1:
- Vertex: O
- Sides: Ray OF and Ray OR

Problem 2:
- Vertex: F
- Sides: Ray FE and Ray FO

Problem 3:
- Vertex: K
- Sides: Ray KJ and Ray KL

Problem 4:
- Vertex: H
- Sides: Ray HO and Ray HJ

Section 2: Name each angle in four ways (Problems 5-8)

For each angle, we can name it using the vertex letter alone and the three-letter notation with the vertex in the middle (which gives two variations).

Problem 5:
- ∠R
- ∠QRS
- ∠SRQ

Problem 6:
- ∠M
- ∠LMN
- ∠NML

Problem 7:
- ∠N
- ∠MNO
- ∠ONM

Problem 8:
- ∠L
- ∠KLM
- ∠MLK

Note: While typically only three distinct names are possible for a single angle (vertex letter and two three-letter combinations), the worksheet likely considers these as the "four ways" requested, possibly including the vertex letter twice or considering the direction of naming.

Section 3: Name all the angles that have V as a vertex (Problems 9-12)

Problem 9:
- Angles with vertex V: ∠DVE, ∠EVF, ∠DVF

Problem 10:
- Angles with vertex V: ∠FVG, ∠GVH, ∠HVJ, ∠FVH, ∠GVJ, ∠FVJ

Problem 11:
- Angles with vertex V: ∠EVO, ∠OVQ, ∠EVQ

Problem 12:
- Angles with vertex V: ∠JVK, ∠KVL, ∠LVM, ∠JVL, ∠KVM, ∠JVM

These solutions provide the required information for each problem on the worksheet.