Angles and Parallel Lines

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Date:

📐 Part 1: Angle Relationships

Remember: When two parallel lines are cut by a transversal (crossing line), special angle relationships are formed:

• Corresponding angles are equal (same position at each intersection)

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

• Alternate exterior angles are equal (outside the parallel lines, on opposite sides)

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

1. When two parallel lines are cut by a transversal, corresponding angles are:

Equal

Different

Add up to 180°

Add up to 90°

2. Alternate interior angles are:

Always 90°

Equal to each other

Add up to 180°

Always different

3. Co-interior angles on the same side of a transversal:

Are equal

Add up to 180°

Add up to 90°

Are always 60°

4. If one angle is 65°, what is its corresponding angle?

Answer: __________

5. If one co-interior angle is 110°, what is the other co-interior angle on the same side?

Working: 180° - 110° = __________

6. Two parallel lines are cut by a transversal. If one alternate interior angle is 45°, the other alternate interior angle is __________

🔍 Part 2: Finding Missing Angles

Method: To find missing angles, identify the relationship first, then use the rule.

7. Lines AB and CD are parallel. A transversal creates an angle of 72°. Find the corresponding angle.

8. In a diagram with parallel lines, one angle measures 125°. What is the alternate interior angle?

Answer: __________

Reason: Alternate interior angles are __________

9. Two co-interior angles are in the ratio 2:3. Find both angles.

Hint: Let the angles be 2x and 3x. Remember co-interior angles add to 180°.

10. If angle a = 3x + 20° and its corresponding angle = 5x - 10°, find the value of x.

Step 1: Set up equation (corresponding angles are equal): ________________

Step 2: Solve for x: x = __________

Step 3: Find the actual angle: __________

11. In parallel lines cut by a transversal, if one exterior angle is 135°, find:

a) Its alternate exterior angle: __________

b) Its corresponding angle: __________

c) The co-interior angle on the same side: __________

12. Two parallel lines are cut by two different transversals. If the angles formed are 2x + 15° and 3x - 25°, and they are alternate interior angles, find x.

⚡ Part 3: Problem Solving

13. Explain why corresponding angles are equal when lines are parallel.

14. A transversal cuts two parallel lines. The ratio of two co-interior angles is 5:4. Calculate both angles.

Let the angles be 5x and 4x.

Equation: 5x + 4x = __________ (because co-interior angles sum to 180°)

Therefore: 9x = 180°, so x = __________

The angles are: __________ and __________

15. True or False: If two lines are cut by a transversal and corresponding angles are equal, then the lines must be parallel.

True

False

Explain your answer: ________________________________

16. Challenge: Three parallel lines are cut by a transversal. If the first angle is 40°, find all the other seven angles at the first intersection point.

17. In your own words, explain the difference between alternate interior and alternate exterior angles.

18. A student claims that vertically opposite angles and alternate angles are the same thing. Are they correct? Explain.