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Angles and Parallel Lines

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Angles and Parallel Lines

Parallel lines with angles diagram

📐 Part 1: Angle Relationships with Parallel Lines

Key Facts to Remember:

• When a transversal crosses parallel lines, it creates special angle pairs

Corresponding angles are equal (same position at each intersection)

Alternate interior angles are equal (on opposite sides, between the parallel lines)

Co-interior angles add up to 180° (on same side, between the parallel lines)

1. Two parallel lines are cut by a transversal. If one angle is 65°, what is the corresponding angle?

25°

65°

115°

180°

2. If alternate interior angles are formed by parallel lines and a transversal, and one angle is 42°, what is its alternate interior angle?

42°

138°

48°

90°

3. Two co-interior angles are formed when parallel lines are cut by a transversal. If one angle is 70°, what is the other co-interior angle?

Hint: Co-interior angles add up to 180°

4. Complete this statement: "Corresponding angles are _____________ when formed by parallel lines and a transversal."

Corresponding angles are _________________ when formed by parallel lines and a transversal.

5. Which angle relationships are created when parallel lines are cut by a transversal? (Select all that apply)

Corresponding angles

Alternate interior angles

Co-interior angles

Vertically opposite angles

6. Calculate the missing angle: If parallel lines are cut by a transversal and one angle is 125°, find its alternate interior angle.
7. Two parallel lines AB and CD are cut by transversal EF. If angle x = 58°, find the corresponding angle y.

Angle y = _______°

Show your reasoning:

🔍 Part 2: Problem Solving with Parallel Lines

8. In the diagram below, lines PQ and RS are parallel. The transversal creates an angle of 73°. Calculate ALL the other angles formed.

Label your angles clearly and show which angle relationships you used.

9. Parallel lines are cut by a transversal. If the ratio of two co-interior angles is 2:3, find both angles.

Hint: Let the angles be 2x and 3x, then use the fact that co-interior angles sum to 180°

10. Two parallel lines are cut by two different transversals. Explain why the corresponding angles formed by each transversal are equal.
11. Find the value of x when parallel lines are cut by a transversal, creating co-interior angles of (3x + 20)° and (2x + 40)°.

x = _______

12. Draw and label a diagram showing parallel lines cut by a transversal. Mark one pair each of corresponding angles, alternate interior angles, and co-interior angles.

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