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

Let’s go step by step through each True/False question based on the diagram of parallel lines L and M cut by transversal N.

We’re told that angle 1 is 125°. Since lines L and M are parallel, we can use angle relationships to find other angles.

First, let’s recall some key angle rules:

- Vertical angles are opposite each other when two lines cross — they are always equal.
- Corresponding angles are in matching corners (like top-left to top-left) — if lines are parallel, they are equal.
- Alternate interior angles are inside the parallel lines and on opposite sides of the transversal — if lines are parallel, they are equal.
- Alternate exterior angles are outside the parallel lines and on opposite sides of the transversal — if lines are parallel, they are equal.
- Supplementary angles add up to 180° — like adjacent angles on a straight line.

Now, let’s label what we know from the diagram:

Angle 1 = 125°

Since angle 1 and angle 3 are vertical angles → angle 3 = 125°

Angle 1 and angle 4 are adjacent on a straight line → angle 4 = 180° - 125° = 55°

Angle 3 and angle 4 are also adjacent → so angle 4 = 55° (same as above)

Because lines L and M are parallel:

- Angle 5 corresponds to angle 1 → angle 5 = 125°
- Angle 6 corresponds to angle 3 → angle 6 = 125°
- Angle 7 corresponds to angle 4 → angle 7 = 55°
- Angle 8 corresponds to angle 2? Wait — actually, angle 8 corresponds to angle 4? Let’s think again.

Actually, better to use:

Angle 1 and angle 5 are corresponding → both 125°

Angle 4 and angle 8 are corresponding → both 55°

Angle 3 and angle 7 are corresponding? No — angle 3 is at top left, angle 7 is bottom left — yes, they are corresponding → both 125°? Wait no — angle 3 is 125°, but angle 7 should be same as angle 4 because they’re corresponding? Let me redraw mentally.

Actually, standard labeling:

Top line L: angles 1 (top right), 2 (top left — not labeled), 3 (bottom left), 4 (bottom right)

Bottom line M: angles 5 (top right), 6 (top left), 7 (bottom left), 8 (bottom right)

Transversal goes from bottom left to top right.

So:

Angle 1 (top right, above L) = 125°

Then:

- Vertical to angle 1 is angle 3 → angle 3 = 125°
- Adjacent to angle 1 is angle 4 → angle 4 = 55°
- Vertical to angle 4 is angle 2 → angle 2 = 55° (but not labeled)

On line M:

- Angle 5 is corresponding to angle 1 → angle 5 = 125°
- Angle 6 is corresponding to angle 3 → angle 6 = 125°
- Angle 7 is corresponding to angle 4 → angle 7 = 55°
- Angle 8 is corresponding to angle 2 → angle 8 = 55°

Also:

- Alternate interior: angle 3 and angle 5? No — angle 3 is below L, left side; angle 5 is above M, right side — not alternate interior.

Alternate interior angles are:

- Between the parallel lines, on opposite sides of transversal.

So:

- Angle 3 (below L, left) and angle 5 (above M, right) — not same side? Actually, angle 3 and angle 5 are on opposite sides of transversal and between the lines → yes, alternate interior → so angle 3 = angle 5 = 125°? But angle 5 is 125°, angle 3 is 125° — yes.

Wait — actually, angle 3 and angle 5 are alternate interior? Let’s see:

Transversal cuts L and M.

Interior region is between L and M.

Angle 3 is below L, left of transversal → inside.

Angle 5 is above M, right of transversal → inside.

And they are on opposite sides of transversal → yes, alternate interior → so they should be equal → both 125° — correct.

Similarly, angle 4 and angle 6: angle 4 is below L, right of transversal; angle 6 is above M, left of transversal → alternate interior → both 55° — yes.

Now let’s answer each question:

1. Angles 1 and 3 are vertical angles.
→ Yes, they are opposite each other at the intersection → TRUE

2. The value of angle 7 is 125 degrees.
→ Angle 7 corresponds to angle 4 → angle 4 is 55° → so angle 7 = 55° → FALSE

3. Angles 1 and 6 are alternate interior angles.
→ Angle 1 is above L, right side; angle 6 is above M, left side — not both interior. Angle 1 is exterior. Alternate interior must be between the lines. So FALSE

4. Angles 3 and 5 are alternate interior angles.
→ As discussed, yes — both between lines, opposite sides of transversal → TRUE

5. Angles 4 and 8 are corresponding angles.
→ Angle 4 is below L, right; angle 8 is below M, right → same relative position → corresponding → TRUE

6. The value of angle 5 is 55 degrees.
→ Angle 5 corresponds to angle 1 → 125° → so FALSE

7. Angles 1 and 7 are alternate exterior angles.
→ Angle 1 is above L, right (exterior); angle 7 is below M, left (exterior). Opposite sides of transversal → yes, alternate exterior → and since lines parallel, they should be equal. Angle 1=125°, angle 7=55° — wait, that doesn’t match!

Wait — hold on. If angle 1 is 125°, and angle 7 is 55°, then they are not equal — but alternate exterior angles should be equal if lines are parallel.

What’s wrong?

Ah — I think I mislabeled.

Let me reassign carefully.

Standard setup:

When two parallel lines are cut by a transversal:

- Corresponding angles are equal.
- Alternate exterior angles are equal.

Angle 1 is given as 125° — let’s assume it’s the top-right angle above line L.

Then:

- Its corresponding angle on line M is angle 5 (top-right above M) → so angle 5 = 125°

- Alternate exterior to angle 1 would be angle 7 (bottom-left below M) — because exterior, opposite side.

But angle 7 should equal angle 1 if they are alternate exterior.

But earlier I said angle 7 = 55° — contradiction.

Where did I go wrong?

Ah — I think I confused the positions.

Let me define:

At intersection with line L:

- Top-right: angle 1 = 125°

- Bottom-right: angle 4

- Bottom-left: angle 3

- Top-left: angle 2 (not labeled)

At intersection with line M:

- Top-right: angle 5

- Bottom-right: angle 8

- Bottom-left: angle 7

- Top-left: angle 6

Now, angle 1 and angle 5 are corresponding → both top-right → so angle 5 = 125°

Angle 1 and angle 7: angle 1 is top-right (exterior), angle 7 is bottom-left (exterior) — and they are on opposite sides of the transversal → so they are alternate exterior angles → should be equal.

But if angle 1 = 125°, then angle 7 should be 125°.

But earlier I thought angle 7 corresponds to angle 4.

Angle 4 is bottom-right at L → 55° (since adjacent to 125°)

Angle 7 is bottom-left at M — which corresponds to angle 2 (top-left at L), not angle 4.

Angle 2 is vertical to angle 4? No.

Angle 1 and angle 2 are adjacent → angle 2 = 180° - 125° = 55°

Angle 2 and angle 6 are corresponding → angle 6 = 55°

Angle 3 and angle 7 are corresponding? Angle 3 is bottom-left at L, angle 7 is bottom-left at M → yes, corresponding → so angle 7 = angle 3 = 125°

I see my mistake earlier.

Let me correct:

Given angle 1 = 125°

Then:

- Angle 3 = vertical to angle 1 = 125°

- Angle 4 = adjacent to angle 1 = 180° - 125° = 55°

- Angle 2 = vertical to angle 4 = 55° (or adjacent to angle 1)

Now for line M:

- Angle 5 = corresponding to angle 1 = 125°

- Angle 6 = corresponding to angle 2 = 55° (since angle 2 is top-left, angle 6 is top-left at M)

- Angle 7 = corresponding to angle 3 = 125° (bottom-left)

- Angle 8 = corresponding to angle 4 = 55° (bottom-right)

Yes, that makes sense.

So:

Angle 1 = 125°

Angle 2 = 55°

Angle 3 = 125°

Angle 4 = 55°

Angle 5 = 125°

Angle 6 = 55°

Angle 7 = 125°

Angle 8 = 55°

Now re-evaluate each question:

1. Angles 1 and 3 are vertical angles. → Yes, opposite at intersection → TRUE

2. The value of angle 7 is 125 degrees. → Yes, as above → TRUE

3. Angles 1 and 6 are alternate interior angles. → Angle 1 is exterior (above L), angle 6 is interior (above M, but between lines? Angle 6 is top-left at M, which is between the lines? Actually, "interior" means between the two parallel lines.

Angle 1 is above line L, so exterior.

Angle 6 is above line M, but since M is the lower line, above M is between L and M? No — if L is top line, M is bottom line, then between them is the region between L and M.

So angle 6 is above M, so if M is the bottom line, above M is towards L, so yes, between the lines — interior.

But angle 1 is above L, so exterior.

Alternate interior angles must both be interior.

So angle 1 is not interior → so not alternate interior with angle 6 → FALSE

4. Angles 3 and 5 are alternate interior angles. → Angle 3 is below L, left side — between lines? Below L is towards M, so yes, interior. Angle 5 is above M, right side — above M is towards L, so between lines, interior. And they are on opposite sides of transversal → yes, alternate interior → TRUE

5. Angles 4 and 8 are corresponding angles. → Angle 4 is bottom-right at L, angle 8 is bottom-right at M → same position → corresponding → TRUE

6. The value of angle 5 is 55 degrees. → Angle 5 = 125° → FALSE

7. Angles 1 and 7 are alternate exterior angles. → Angle 1 is top-right (exterior), angle 7 is bottom-left (exterior), opposite sides of transversal → yes, alternate exterior → and both 125° → TRUE

8. Angles 6 and 8 are corresponding angles. → Angle 6 is top-left at M, angle 8 is bottom-right at M — different positions, not corresponding. Corresponding would be same relative position at different intersections. Angle 6 corresponds to angle 2, angle 8 corresponds to angle 4. So 6 and 8 are not corresponding → FALSE

9. Angles 1 and 6 are supplementary angles. → Angle 1 = 125°, angle 6 = 55° → 125 + 55 = 180 → yes, supplementary → TRUE

10. Angles 4 and 8 are supplementary angles. → Angle 4 = 55°, angle 8 = 55° → 55 + 55 = 110 ≠ 180 → FALSE

Now summarize:

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