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work out the size of angle f. Give your answer in degrees

To find the size of angle \( f \), we need to utilize the properties of angles formed by parallel lines and a transversal. Here’s the step-by-step solution:

1. **Identify Corresponding Angles**: Since the lines are parallel, corresponding angles are equal.
2. **Identify Adjacent Angles on a Straight Line**: Adjacent angles on a straight line sum to 180°.
3. **Calculate Unknown Angles**: Use the sum of angles around a point and adjacent angles to find \( f \).

**Step-by-Step Solution:**

1. **Angles on a Straight Line**:
   - The angles \( 68^\circ \) and \( 112^\circ \) are on a straight line, so they add up to \( 180^\circ \):
     \[
     68^\circ + 112^\circ = 180^\circ
     \]

2. **Calculate Vertical Angles**:
   - The angle vertically opposite \( 112^\circ \) is also \( 112^\circ \) (vertical angles are equal).

3. **Corresponding Angles**:
   - The angle corresponding to \( 76^\circ \) (alternate interior angle to \( f \)) is \( 76^\circ \).

4. **Sum of Angles in the Triangle**:
   - If we consider the angles around the point where \( f \) is located, they must sum up to \( 360^\circ \).

Given:
   - One angle is \( 112^\circ \) (from the vertical angle calculation).
   - Another angle is \( 68^\circ \) (on the same line as \( f \)).

5. **Calculate \( f \)**:
   - Since the sum of angles around a point is \( 360^\circ \), and we know \( 76^\circ + 68^\circ + 112^\circ = 256^\circ \), the angle \( f \) can be calculated as:
     \[
     f = 360^\circ - 256^\circ = 104^\circ
     \]

Thus, the size of angle \( f \) is \( 104^\circ \).

Would you like more details or have any other questions?

Here are 5 numbered questions you might ask next:
1. How do you determine the angles formed by parallel lines and a transversal?
2. What are vertical angles and how do they relate to each other?
3. Can you explain corresponding angles in more detail?
4. How do you solve for angles when multiple lines intersect?
5. What are supplementary angles and how are they used in angle calculations?

**Tip**: Remember that angles on a straight line add up to 180°, and angles around a point add up to 360°. This is useful in many geometric problems involving parallel lines and transversals.

Learn how to find the size of angle f using geometric principles involving parallel lines and a transversal. This problem covers corresponding angles, angles on a straight line, and angles around a point. Suitable for students in Grades 7-9.

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