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Calculate the unknown angles in each of the following, giving reasons for all your statements.

Let's solve the unknown angles in each diagram step by step. I'll refer to the diagrams in the image based on their position (from top to bottom and left to right).

### 1. Top Left Diagram:
- **Given:** One angle is marked as \(47^\circ\).
- **Solution:** This is a right-angled triangle, so the other angle on the same straight line is \(180^\circ - 47^\circ = 133^\circ\).

### 2. Top Right Diagram:
- **Given:** The diagram shows two intersecting lines.
- **Solution:** The angle across from the one marked \(67^\circ\) will also be \(67^\circ\) because vertically opposite angles are equal.

### 3. Middle Left Diagram:
- **Given:** Two angles are vertically opposite, one marked as \(58^\circ\).
- **Solution:** The other angle will also be \(58^\circ\) since vertically opposite angles are equal.

### 4. Middle Right Diagram:
- **Given:** An angle of \(37^\circ\) is marked.
- **Solution:** The angle adjacent on the straight line will be \(180^\circ - 37^\circ = 143^\circ\).

### 5. Bottom Left Diagram:
- **Given:** There are two angles on a straight line, with one marked \(114^\circ\).
- **Solution:** The unknown angle is \(180^\circ - 114^\circ = 66^\circ\).

### 6. Bottom Right Diagram:
- **Given:** Two angles on a straight line, with one marked \(146^\circ\).
- **Solution:** The other angle is \(180^\circ - 146^\circ = 34^\circ\).

### Summary of Solutions:
1. \(133^\circ\) (Right angle)
2. \(67^\circ\) (Vertically opposite)
3. \(58^\circ\) (Vertically opposite)
4. \(143^\circ\) (Straight angle)
5. \(66^\circ\) (Straight angle)
6. \(34^\circ\) (Straight angle)

Would you like more details on any of these solutions?

Here are some related questions:
1. How do you calculate vertically opposite angles?
2. Why do angles on a straight line sum up to \(180^\circ\)?
3. What are supplementary angles?
4. Can you find the value of unknown angles in a triangle?
5. What is the significance of complementary angles?
6. How can you find angles using the sum of interior angles of a polygon?
7. What are corresponding angles and how are they calculated?
8. How do you determine alternate interior angles?

**Tip:** Always remember that the angles on a straight line add up to \(180^\circ\), and vertically opposite angles are always equal!

Learn how to calculate unknown angles in geometric diagrams step-by-step. Understand the concepts of vertical angles and straight angles. Suitable for students in Grades 7-9, this problem explores basic geometric properties and angle relationships.

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