https://file.aiquickdraw.com/mathbot/file/1725574726611c2tanw1z.jpg

The image is of a geometry worksheet titled "Math 2: Geometry - Angle Addition." Let's break down each part of the exercise and solve them step-by-step.

### Problem Description:
The worksheet contains a diagram with several intersecting lines, labeled points, and angles. The questions are related to naming and calculating angles and their measures.

### Steps to Solve:

1. **a) Name the vertex of ∠1:**
   - The vertex of an angle is the common point where the two rays of the angle meet. We need to identify the common point for ∠1.

2. **b) Name the sides of ∠2:**
   - The sides of an angle are the rays that make up the angle. We need to determine the rays that form ∠2.

3. **c) Write another name for ∠5:**
   - Another name for an angle can be expressed by using three points: a point on one ray, the vertex, and a point on the other ray. We need to identify these three points for ∠5.

4. **d) Classify each angle:**
   - Classify the angles listed as acute, obtuse, right, or straight.

5. **e) Name a pair of vertical angles:**
   - Vertical angles are the angles opposite each other when two lines intersect. We need to identify a pair of these angles from the diagram.

6. **f) If m∠ABD = 45° and m∠DBC = 105°, find m∠ABC:**
   - Use the Angle Addition Postulate, which states that if a point D lies in the interior of ∠ABC, then m∠ABC = m∠ABD + m∠DBC.

### Solution:

Let me analyze the image further to extract precise details for each part. Then I will provide specific answers for each question based on the given geometry diagram.

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**Would you like me to continue with detailed solutions for each part?** Here are some related questions to expand your understanding:

1. How do you determine the vertex of an angle?
2. What is the difference between complementary and supplementary angles?
3. How do you classify angles as acute, obtuse, right, or straight?
4. What are vertical angles, and why are they always equal?
5. How can the Angle Addition Postulate be used to solve for unknown angles?

**Tip:** When solving geometry problems, always start by carefully examining the diagram and identifying all known and unknown elements.

Use the diagram to complete each part: a) Name the vertex of ∠1. b) Name the sides of ∠2. c) Write another name for ∠5. d) Classify each angle (∠5, ∠6). e) Name a pair of vertical angles. f) If m∠ABD = 45° and m∠DBC = 105°, find m∠ABC.

This geometry worksheet covers concepts like identifying vertices, naming angle sides, classifying angles, and applying the Angle Addition Postulate. Suitable for students in Grades 7-9.

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