https://file.aiquickdraw.com/mathbot/file/1726177932679n3gf1qll.jpg

Let's go step-by-step to solve for the angles in the diagram based on the information provided.

### Step 1: Identify the known angles
From the image:
- Angle 1 is \( 75^\circ \).
- Angle 2 needs to be found.
- Angle 3 is \( 68^\circ \).
- Angle 4 needs to be found.
- Angle 5 needs to be found.
- Angle 6 needs to be found.

### Step 2: Use relationships between angles
1. **Angle 1 and Angle 2**: These are supplementary because they form a linear pair (i.e., on a straight line). The sum of supplementary angles is \( 180^\circ \).
   \[
   \text{Angle 1} + \text{Angle 2} = 180^\circ
   \]
   \[
   75^\circ + \text{Angle 2} = 180^\circ \quad \Rightarrow \quad \text{Angle 2} = 180^\circ - 75^\circ = 105^\circ
   \]
   **So, Angle 2 = 105°.**

2. **Angle 3 and Angle 4**: These are supplementary because they also form a linear pair.
   \[
   \text{Angle 3} + \text{Angle 4} = 180^\circ
   \]
   \[
   68^\circ + \text{Angle 4} = 180^\circ \quad \Rightarrow \quad \text{Angle 4} = 180^\circ - 68^\circ = 112^\circ
   \]
   **So, Angle 4 = 112°.**

3. **Angle 5 and Angle 4**: These angles are vertically opposite, which means they are equal.
   \[
   \text{Angle 5} = \text{Angle 4} = 112^\circ
   \]
   **So, Angle 5 = 112°.**

4. **Angle 6**: Since Angle 5 and Angle 6 form a linear pair, they are supplementary.
   \[
   \text{Angle 5} + \text{Angle 6} = 180^\circ
   \]
   \[
   112^\circ + \text{Angle 6} = 180^\circ \quad \Rightarrow \quad \text{Angle 6} = 180^\circ - 112^\circ = 68^\circ
   \]
   **So, Angle 6 = 68°.**

### Summary of the angles:
- Angle 1 = \( 75^\circ \)
- Angle 2 = \( 105^\circ \)
- Angle 3 = \( 68^\circ \)
- Angle 4 = \( 112^\circ \)
- Angle 5 = \( 112^\circ \)
- Angle 6 = \( 68^\circ \)

Would you like more details on any specific part of the solution? 

Here are some follow-up questions to explore:
1. What is the rule for determining if angles are supplementary?
2. How are vertically opposite angles defined, and why are they equal?
3. How would you find the value of angles in other geometric shapes, such as triangles?
4. How can we apply these angle relationships in real-world situations?
5. How would the solution change if one angle's value were altered?

**Tip:** In geometry, understanding the relationships between angles (like supplementary, complementary, and vertically opposite) helps solve problems more efficiently.

Find Angle 2, Angle 4, Angle 5, and Angle 6 based on the provided diagram with given angles (75° and 68°).

Learn how to find unknown angles based on given angles in a diagram. This problem involves applying the supplementary angle theorem and vertical angle theorem. Suitable for Grades 6-8.

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