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Let me help you with the math problems presented in the image. The picture shows multiple problems involving angles with transversal lines and parallel lines.

Here’s a breakdown of the problems:

### Problem 3:
Find the sizes of angles \(a\), \(b\), \(c\), and \(d\) based on a diagram that shows intersecting lines.

The diagram shows that \(a = 140^\circ\), and the remaining angles are calculated using the fact that:
- Vertically opposite angles are equal.
- Adjacent angles on a straight line sum up to \(180^\circ\).

Hence:
- \(b = 180^\circ - a = 180^\circ - 140^\circ = 40^\circ\),
- \(c = b = 40^\circ\) (as they are vertically opposite),
- \(d = 180^\circ - b = 180^\circ - 40^\circ = 140^\circ\) (as it is supplementary to angle \(b\)).

### Problem 4:
Find the sizes of all the angles in the given figure.

The figure shows intersecting lines with one given angle \( \angle FKC = 130^\circ \). Based on the rules of intersecting lines:
- Vertically opposite angles are equal, so \( \angle FKE = 130^\circ \),
- Adjacent angles on a straight line sum up to \(180^\circ\), so \( \angle KBE = 50^\circ \) and \( \angle KAC = 50^\circ \),
- \( \angle KFD = \angle FKE = 130^\circ \).

### Problem 5:
Find the sizes of all angles in the diagram involving two transversals crossing two sets of parallel lines.

Here, \( \angle AMP = 95^\circ \). Using the properties of parallel lines cut by a transversal:
- Corresponding angles are equal,
- Alternate interior angles are equal,
- Consecutive interior angles sum up to \(180^\circ\).

Let me know if you'd like a more detailed explanation for any of these problems, and here are some additional questions that you might find useful for further understanding:

1. Why are vertically opposite angles always equal?
2. How do corresponding angles behave when a transversal crosses parallel lines?
3. What is the sum of the interior angles on the same side of a transversal when it intersects parallel lines?
4. How are alternate interior angles identified when two parallel lines are crossed by a transversal?
5. In which scenarios do you use the rule that adjacent angles on a straight line sum to 180°?

**Tip**: Always check if two lines are parallel, as this can simplify angle calculations when dealing with transversals.

Find the sizes of all angles in the given figures, including angles formed by intersecting and parallel lines.

Learn how to solve angle problems involving intersecting lines and parallel lines cut by transversals. This solution explains the use of vertically opposite angles, supplementary angles, and parallel line theorems. Suitable for students in Grades 6-8.

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