Parallel and Perpendicular Lines with a Trasnversal Line worksheet ... - Free Printable

Let’s solve each problem step by step. Remember: Lines A and B are parallel, and line C is a transversal (a line that crosses both). We’ll use angle rules like:

- Vertical angles are equal (opposite angles when two lines cross).
- Corresponding angles are equal (same position on each parallel line).
- Alternate interior angles are equal (inside the parallels, opposite sides of transversal).
- Supplementary angles add up to 180° (when they form a straight line).

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Problem 1

We’re given an angle of 85° next to Angle 1. They form a straight line → so they are supplementary.

→ Angle 1 = 180° - 85° = 95°

Angle 2 is directly below Angle 1, on the other parallel line. Since lines A and B are parallel, Angle 2 corresponds to the 85° angle (they’re in the same relative position) → so Angle 2 = 85°

Wait — let’s double-check. Actually, looking at the diagram:

The 85° angle and Angle 1 are adjacent on a straight line → yes, supplementary → Angle 1 = 95°.

Angle 2 is vertically opposite to the 85° angle? No — actually, Angle 2 is on the lower line, same side as the 85° angle but below. That makes them corresponding angles → so Angle 2 = 85°.

✔ Correct.

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Problem 2

Given: 122° angle next to Angle 1 → they form a straight line → supplementary.

→ Angle 1 = 180° - 122° = 58°

Angle 2 is on the lower line, same side as the 122° angle → corresponding angles → so Angle 2 = 122°

Wait — check again. The 122° angle is above line A, right side. Angle 2 is below line B, left side? Let me visualize.

Actually, in standard diagrams like this, if 122° is on top right, then Angle 2 (on bottom left) would be alternate exterior or something else?

Better approach: Look at vertical angles and corresponding.

Actually, Angle 2 is vertically opposite to the angle that corresponds to 122°? Hmm.

Alternative: The angle directly across from 122° (vertical angle) is also 122°, and that’s on the same side as Angle 2? Not quite.

Let’s think differently.

In diagram 2:

- The 122° angle and Angle 1 are adjacent → sum to 180° → Angle 1 = 58° ✔️

Now, Angle 2 is on the lower line, same side of transversal as the 122° angle → that means they are corresponding angles → so Angle 2 = 122° ✔️

Yes.

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Problem 3

Given: 72° angle on top right.

Angle 1 is on the bottom left — that’s alternate interior with the 72° angle? Wait — no.

Actually, 72° is on top right. Angle 1 is on bottom left — those are alternate exterior? Or maybe not.

Better: The angle directly across from 72° (vertical angle) is also 72°, and that’s on the top left.

Then, Angle 1 is on the bottom left — that’s corresponding to the top left angle → so Angle 1 = 72°? But wait, that doesn’t match typical labeling.

Looking at diagram 3:

Label says “72°” near top right. Then Angle 1 is labeled on the bottom left intersection, between line B and C. Angle 2 is on the bottom right.

Actually, 72° and Angle 1 are alternate interior angles? Let’s see:

If 72° is above line A, right side, then the alternate interior angle would be below line B, left side — which is exactly where Angle 1 is! So yes — alternate interior angles are equal → Angle 1 = 72°

Then Angle 2 is adjacent to Angle 1 on the straight line → supplementary → Angle 2 = 180° - 72° = 108°

Wait — but in the diagram, Angle 2 is labeled on the same side as the 72°? Let me recheck.

Actually, in many such diagrams, Angle 1 and Angle 2 are on the same intersection point on line B.

So if Angle 1 is 72°, and Angle 2 is next to it on the straight line → then yes, Angle 2 = 108°.

But let’s confirm with another method.

The 72° angle has a vertical angle also 72° (top left). Then, the angle corresponding to that on line B (bottom left) is Angle 1 → so Angle 1 = 72°.

Then Angle 2 is adjacent → 180 - 72 = 108°.

✔ Correct.

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Problem 4

Given: 140° angle on bottom right.

Angle 1 is on top right — that’s corresponding to the 140° angle? Yes — same position on each parallel line → so Angle 1 = 140°

Angle 2 is on top left — adjacent to Angle 1 on the straight line → supplementary → Angle 2 = 180° - 140° = 40°

Alternatively, Angle 2 is alternate interior to the angle that’s vertical to 140°? Vertical to 140° is also 140° (bottom left), then alternate interior to that would be top right — which is Angle 1. So Angle 2 is adjacent to Angle 1 → still 40°.

✔ Correct.

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## Final Answer:

Problem 1:
Angle 1 = 95°
Angle 2 = 85°

Problem 2:
Angle 1 = 58°
Angle 2 = 122°

Problem 3:
Angle 1 = 72°
Angle 2 = 108°

Problem 4:
Angle 1 = 140°
Angle 2 = 40°