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In this diagram, you are tasked with finding the values of angles \( a \) and \( b \). The diagram shows several lines intersecting at point \( A \), creating different angles. Here's how we can approach the problem:

### Step 1: Identify known angles and relationships
- The angle labeled \( 25^\circ \) is provided between lines \( E \) and \( F \).
- It is clear from the figure that lines \( F \) and \( D \), \( E \) and \( B \), as well as other pairs, are forming vertically opposite angles or linear pairs.

### Step 2: Use the linear pair rule
A linear pair of angles on a straight line always sums to \( 180^\circ \). Let's apply this concept:
- Angle \( a \) and \( 25^\circ \) form a linear pair since they lie on the same straight line. Therefore:
  \[
  a + 25^\circ = 180^\circ
  \]
  Solving for \( a \):
  \[
  a = 180^\circ - 25^\circ = 155^\circ
  \]

### Step 3: Use the vertical angles rule
- Angle \( b \) is vertically opposite to the angle adjacent to \( a \), meaning:
  \[
  b = 90^\circ
  \]
  This is because line \( BC \) is perpendicular to line \( EF \), creating a right angle (\( 90^\circ \)).

### Final Values:
- \( a = 155^\circ \)
- \( b = 90^\circ \)

Would you like further explanation on the reasoning behind vertical angles or linear pairs?

### Related questions:
1. What is the sum of all angles around point \( A \)?
2. How do we know that \( BC \) is perpendicular to \( EF \)?
3. Can angles \( a \) and \( b \) ever change without modifying the lines?
4. What would the relationship between \( a \) and \( b \) be if they were on the same side of a straight line?
5. Can you calculate the value of any other angles in the diagram using these methods?

### Tip:
Always look for linear pairs and vertical angles when dealing with intersecting lines—they simplify many angle calculations.

Find the value of angles a and b from the given diagram with intersecting lines and a marked 25° angle.

Learn how to calculate angles a and b from a diagram involving intersecting lines and a given 25° angle. This solution uses the linear pair and vertical angles theorems, suitable for Grades 7-10.

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