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To determine the sizes of the given angles \( L1, L2, B1, B2, F1, F2, G1, G2 \) from the diagram, we can analyze the geometric properties and relationships like supplementary angles, vertically opposite angles, and corresponding angles in intersecting lines. Let's break down the reasoning:

### Given Angles:
1. \( \angle CEB = 44^\circ \)
2. \( \angle LEB = 68^\circ \)
3. \( \angle FTA = 76^\circ \)
4. \( \angle GDR = 120^\circ \)

### Step-by-Step Angle Calculation:
#### 1. **Angle \( L1 \) (Angle \( \angle LEB \))**:
   - This angle is already given as \( 68^\circ \).
   - **Reason**: It is provided directly in the diagram.

#### 2. **Angle \( L2 \)**:
   - \( L2 \) is vertically opposite to \( L1 \) at the intersection of lines \( EF \) and \( BD \).
   - Vertically opposite angles are equal.
   - Therefore, \( L2 = 68^\circ \).
   - **Reason**: Vertically opposite angles.

#### 3. **Angle \( B1 \) (Angle \( \angle BEC \))**:
   - The line \( EC \) is a straight line, and \( L1 \) and \( B1 \) are adjacent angles on this line.
   - These angles are supplementary, so they sum to \( 180^\circ \).
   - \( B1 = 180^\circ - 68^\circ = 112^\circ \).
   - **Reason**: Supplementary angles on a straight line.

#### 4. **Angle \( B2 \)**:
   - \( B2 \) is vertically opposite to \( B1 \), so \( B2 = 112^\circ \).
   - **Reason**: Vertically opposite angles.

#### 5. **Angle \( F1 \)**:
   - \( F1 \) and \( F2 \) are on a straight line.
   - Given that \( \angle FTA = 76^\circ \), and these angles are supplementary, they add to \( 180^\circ \).
   - \( F1 = 180^\circ - 76^\circ = 104^\circ \).
   - **Reason**: Supplementary angles.

#### 6. **Angle \( F2 \)**:
   - \( F2 \) is equal to \( 76^\circ \) because it was given directly in the diagram.
   - **Reason**: Given.

#### 7. **Angle \( G1 \)**:
   - \( G1 \) and \( G2 \) are on a straight line, and they sum to \( 180^\circ \).
   - Since \( G2 \) is given as \( 120^\circ \), we can calculate:
   - \( G1 = 180^\circ - 120^\circ = 60^\circ \).
   - **Reason**: Supplementary angles.

#### 8. **Angle \( G2 \)**:
   - \( G2 \) is given as \( 120^\circ \) in the diagram.
   - **Reason**: Given.

### Summary of Angle Measurements:
- \( L1 = 68^\circ \)
- \( L2 = 68^\circ \)
- \( B1 = 112^\circ \)
- \( B2 = 112^\circ \)
- \( F1 = 104^\circ \)
- \( F2 = 76^\circ \)
- \( G1 = 60^\circ \)
- \( G2 = 120^\circ \)

Would you like a deeper explanation of any particular angle or how these relationships work?

Here are 5 relative questions you might find useful:

1. Why are vertically opposite angles always equal when two lines intersect?
2. What are the conditions for two angles to be supplementary?
3. Can you identify other pairs of vertically opposite angles in the diagram?
4. How can parallel lines and transversals be used to find missing angles in similar diagrams?
5. How do we prove that adjacent angles on a straight line are supplementary?

**Tip**: Always look for straight lines and intersections in diagrams as they provide key relationships like supplementary and vertically opposite angles.

Use the information in the diagram to determine the size of the following angles: L1, L2, B1, B2, F1, F2, G1, G2. Give reasons for all statements.

This problem covers key concepts of angles formed by intersecting lines, including vertically opposite and supplementary angles. Learn how to calculate angles such as L1, L2, B1, B2, F1, F2, G1, and G2 with step-by-step reasoning. Suitable for students in Grades 7-10.

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