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In the given diagram, we are tasked with finding the values of angles \( a \), \( b \), and \( c \). Here's how to approach it:

### 1. Using Parallel Line Properties
We are told that lines \( PQ \) and \( RS \) are parallel. This allows us to use the properties of corresponding, alternate interior, and co-interior angles to solve for \( a \), \( b \), and \( c \).

#### Step 1: Find angle \( a \)
Angle \( a \) is formed at the intersection of the transversal and parallel lines. We are given that the angle adjacent to it (in a corresponding position across the transversal) is \( 70^\circ \).

- Since these are corresponding angles, \( a = 70^\circ \).

#### Step 2: Find angle \( b \)
We see that angle \( b \) is vertically opposite the angle \( 65^\circ \) (this is clearly marked on the diagram).

- Vertically opposite angles are equal, so \( b = 65^\circ \).

#### Step 3: Find angle \( c \)
Angle \( c \) is part of a linear pair with angle \( b \) (which is \( 65^\circ \)). A linear pair of angles adds up to \( 180^\circ \).

- Therefore, \( c = 180^\circ - 65^\circ = 115^\circ \).

### Final Answers:
- \( a = 70^\circ \)
- \( b = 65^\circ \)
- \( c = 115^\circ \)

Would you like further explanation or details on these concepts?

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Here are some follow-up questions to extend your understanding:
1. What are alternate interior angles, and how can they be identified in parallel line diagrams?
2. Can you explain why vertically opposite angles are always equal?
3. How do we determine if angles form a linear pair?
4. In what other cases can angles add up to \( 180^\circ \)?
5. How does the sum of angles around a point relate to this problem?

**Tip**: Always look for corresponding and alternate interior angles when working with parallel lines. These relationships are key to solving most angle problems.

Find the values of a, b, and c in Diagram 7, where PQ and RS are parallel lines.

Learn how to calculate the angles a, b, and c formed by a transversal crossing parallel lines in Diagram 7. This problem explores corresponding angles, vertically opposite angles, and linear pairs of angles, key concepts in geometry. Suitable for Grades 8-10.

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