True/False worksheet on angles formed by parallel lines cut by a transversal.

Let’s go through each True/False question one by one, using the diagram and geometry rules about parallel lines cut by a transversal.

We’re told:
- Lines L and M are parallel.
- Line N is the transversal.
- Angle 1 = 125° (given in diagram).

Remember key angle relationships:

✔ Vertical angles → equal
✔ Corresponding angles → equal (when lines are parallel)
✔ Alternate interior angles → equal (when lines are parallel)
✔ Alternate exterior angles → equal (when lines are parallel)
✔ Supplementary angles → add up to 180° (like adjacent angles on a straight line)

Also, since angle 1 = 125°, we can find others:

- Angle 3 = vertical to angle 1 → also 125°
- Angle 2 (not labeled but opposite angle 1) would be 55° — but we don’t need it.
- Angle 4 = adjacent to angle 1 → 180° - 125° = 55°
- Angle 5 = corresponding to angle 1 → 125° (since L || M)
- Angle 6 = alternate interior to angle 4 → 55°
- Angle 7 = vertical to angle 5 → 125°
- Angle 8 = corresponding to angle 4 → 55°

Now let’s check each statement:

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1. Angles 1 and 3 are vertical angles.
→ Yes! They are opposite each other at the intersection. Vertical angles are always equal.
✔️ TRUE

2. The value of angle 7 is 125 degrees.
→ Angle 7 is vertical to angle 5. Angle 5 corresponds to angle 1 (125°), so angle 5 = 125°, then angle 7 = 125°.
✔️ TRUE

3. Angles 1 and 6 are alternate interior angles.
→ Alternate interior angles are between the two parallel lines and on opposite sides of the transversal.
Angle 1 is above line L, outside — not interior. So no.
✘ FALSE

4. Angles 3 and 5 are alternate interior angles.
→ Angle 3 is between L and M? No — angle 3 is below line L, above line M? Wait — actually, angle 3 is between the two lines? Let’s see:
Line L is top, line M is bottom. Transversal cuts them.
Angle 3 is below line L, above line M → that’s between the lines.
Angle 5 is above line M, below line L → also between the lines.
And they’re on opposite sides of the transversal → yes, alternate interior.
✔️ TRUE

Wait — correction: Actually, angle 3 is on the left side of transversal, angle 5 is on the right side → yes, alternate interior. And since lines are parallel, they should be equal. Angle 3 = 125°, angle 5 = 125° → matches.
✔️ TRUE

5. Angles 4 and 8 are corresponding angles.
→ Corresponding angles are in the same relative position at each intersection.
Angle 4 is below line L, right side of transversal.
Angle 8 is below line M, right side of transversal → yes, corresponding.
✔️ TRUE

6. The value of angle 5 is 55 degrees.
→ Angle 5 corresponds to angle 1 → which is 125°. So angle 5 = 125°, not 55°.
✘ FALSE

7. Angles 1 and 7 are alternate exterior angles.
→ Alternate exterior angles are outside the parallel lines and on opposite sides of the transversal.
Angle 1 is above line L, right side → exterior.
Angle 7 is below line M, left side → exterior.
Opposite sides → yes.
✔️ TRUE

8. Angles 6 and 8 are corresponding angles.
→ Angle 6 is above line M, left side.
Angle 8 is below line M, right side → different positions. Not corresponding.
Actually, angle 6 and angle 2 (if labeled) would be corresponding.
Angle 6 and angle 8 are adjacent? No — they’re on same line, different sides.
They are actually vertical? No — angle 6 and 8 are on the same side of transversal? Wait — angle 6 is left, angle 8 is right → not vertical.
Actually, angle 6 and angle 8 are supplementary? Maybe, but not corresponding.
Corresponding to angle 6 would be angle 2 (above line L, left).
So angle 6 and 8 are NOT corresponding.
✘ FALSE

9. Angles 1 and 6 are supplementary angles.
→ Angle 1 = 125°, angle 6 = 55° (as calculated earlier).
125 + 55 = 180 → yes, supplementary.
✔️ TRUE

10. Angles 4 and 8 are supplementary angles.
→ Angle 4 = 55°, angle 8 = 55° → 55 + 55 = 110 ≠ 180 → not supplementary.
Also, they are corresponding angles → so they are equal, not supplementary.
✘ FALSE

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Final Answers:

1. True
2. True
3. False
4. True
5. True
6. False
7. True
8. False
9. True
10. False

Final Answer:
1. True
2. True
3. False
4. True
5. True
6. False
7. True
8. False
9. True
10. False