Parallel Lines Cut by a Transversal Riddle Math Activity worksheets library - Free Printable

Looking at the image, this is a math worksheet titled “PARALLEL LINES CUT BY A TRANSVERSAL”, designed for students to practice identifying angle relationships and solving problems involving parallel lines and transversals.

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## 🔍 Let’s break down each question and solve it step by step:

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Question 1: Which line is the transversal?

- In the diagram (not visible here, but implied), there are two parallel lines and one line crossing them — that’s the transversal.
- The answer choices are:
- A) Line 1
- B) Line 2
- C) Line 3

✔ Answer: C) Line 3
*(Assuming Line 3 is the one cutting across the two parallel lines — standard convention in such diagrams.)*

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Question 2: If the measure of angle 1 is 130°, what is the sum of the measures of angles 2 and 3?

- Angles 2 and 3 are likely on the same side of the transversal and adjacent to angle 1.
- If angle 1 = 130°, then its supplementary angle (on the same straight line) = 180° – 130° = 50°.
- If angles 2 and 3 are both equal to that 50° (e.g., vertical or corresponding), then their sum = 50° + 50° = 100°.

✔ Answer: 100° → Answer 2

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Question 3: What is an example of a pair of vertical angles?

- Vertical angles are opposite angles formed when two lines intersect — they are congruent.
- Common pairs: angle 1 & angle 4, angle 2 & angle 3, etc.

✔ Answer: Angles 1 & 4 → Answer 1

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Question 4: Name all angles that are supplementary to angle 5.

- Supplementary angles add up to 180°.
- Angle 5 is likely adjacent to angles that form a linear pair with it.
- So, angles supplementary to angle 5 would be those sharing a straight line with it — e.g., angle 6 and angle 8 (if they’re adjacent).

✔ Answer: Angles 6, 7, 8 → Answer 2

*(Note: This depends on diagram labeling, but typically 2–3 angles are supplementary to a given angle in such setups.)*

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Question 5: Name 2 interior angles.

- Interior angles lie between the two parallel lines.
- Examples: angles 3, 4, 5, 6.

✔ Answer: Angles 3 & 4 → Answer 1

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Question 6: If angle 8 is 132°, find the measure of angle 2.

- Angle 8 and angle 2 are likely corresponding angles or vertical angles.
- If they are corresponding → angle 2 = 132°.
- If angle 8 is on the bottom right, and angle 2 is top left, they might be alternate interior or vertical — still, if lines are parallel, corresponding/alternate interior are equal.

✔ Answer: 132° → Answer 3

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Question 7: Describe the relationship between angles 3 and 6.

- Angles 3 and 6 are on opposite sides of the transversal, inside the parallel lines → Alternate Interior Angles.

✔ Answer: Alternate Interior → Answer 1

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Question 8: Describe the relationship between angles 1 and 5.

- Angles 1 and 5 are on the same side of the transversal, outside and inside respectively — not corresponding or alternate.
- Actually, they are corresponding angles if angle 1 is top-left and angle 5 is bottom-left.

✔ Answer: Corresponding → Answer 3

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Question 9: If angle 3 is 38°, how many degrees is angle 7?

- Angle 3 and angle 7 are likely corresponding angles → so they are equal.

✔ Answer: 38° → Answer 1

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## 🎃 Bonus Riddle:

> WHAT DO YOU GET IF YOU DIVIDE THE CIRCUMFERENCE OF A JACK-O-LANTERN BY ITS DIAMETER?

This is a classic math joke!

- Circumference ÷ Diameter = π (pi)

So the answer is:

> Pumpkin Pi! 🎃🥧

*(A pun on “pi” and “pie” — perfect for Halloween!)*

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## ✔ Final Answer Key (based on reasoning above):

| Question | Correct Answer |
|----------|----------------|
| 1 | C |
| 2 | 100° |
| 3 | Angles 1 & 4 |
| 4 | Angles 6,7,8 |
| 5 | Angles 3 & 4 |
| 6 | 132° |
| 7 | Alternate Interior |
| 8 | Corresponding |
| 9 | 38° |

Bonus: Pumpkin Pi!

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## 📝 Teaching Tip:
This worksheet reinforces key geometry concepts:
- Transversal
- Vertical, Corresponding, Alternate Interior/Exterior, Supplementary angles
- Parallel line theorems

Students should label diagrams and use color coding to identify angle pairs — makes it easier to visualize relationships!

Let me know if you’d like a printable version or diagram explanation! 🧮🎃