Angle Relationships Worksheet - Identify types of angles formed by intersecting lines.

Let's solve each problem step by step based on the image you provided. The worksheet asks us to identify angle relationships in two categories:

1. Complementary, supplementary, vertical, or adjacent (problems 1–6)
2. Alternate interior, corresponding, or alternate exterior (problems 7–10)

We'll go through each one.

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Part 1: Name the relationship: complementary, supplementary, vertical, or adjacent

#### 1)
Two angles labeled ∠1 and ∠2 are formed by two intersecting lines, sharing a common vertex and side, but not overlapping.

- They share a common side and vertex.
- They are next to each other and form a straight line together? No — they are not forming a straight line.
- Actually, looking at the diagram: the two angles are adjacent because they share a common side and vertex, and do not overlap.

✔ Answer: Adjacent

> *Note:* Since they don't appear to add up to 90° or 180°, and aren't opposite, "adjacent" is correct.

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#### 2)
Two angles labeled ∠1 and ∠2 are formed by two rays from a point, with no shared side. But they seem to be on a straight line?

Wait — actually, this appears to be two angles that are adjacent, sharing a common ray and vertex, and together forming a straight line.

So:
- They are adjacent
- And their sum is 180° → Supplementary

But the question only wants one relationship.

They are adjacent and supplementary, but since “adjacent” is more specific about location, and “supplementary” refers to sum, we need to see what’s being asked.

But the instruction says: “Name the relationship: complementary, supplementary, vertical, or adjacent.”

So pick one of these four.

Since they form a straight line, they are supplementary.

But are they adjacent? Yes — they share a side.

But if they are adjacent and form a straight line, they are linear pair, which is a type of supplementary adjacent angles.

But the choices are limited.

So both adjacent and supplementary apply.

But which one should we choose?

In such cases, if they are adjacent and form a linear pair, supplementary is often the intended answer.

But let’s check the diagram carefully.

Looking at the image: Two rays from a point, one going left, one going right, and another ray splitting them into two angles.

Actually, it looks like two angles sharing a common side and vertex, and together making a straight line → linear pair, so supplementary.

✔ Answer: Supplementary

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#### 3)
Two intersecting lines forming an "X". Angles labeled ∠1 and ∠2 are opposite each other.

These are vertical angles.

✔ Answer: Vertical

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#### 4)
Two angles labeled ∠1 and ∠2, sharing a common vertex and side, and there's a square symbol at the corner — indicating a right angle.

The two angles are next to each other, and together make a right angle (90°), so they are complementary.

Also, they are adjacent.

But again, pick the most accurate one.

They add to 90° → complementary

✔ Answer: Complementary

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#### 5)
Two angles labeled ∠1 and ∠2, sharing a common vertex and side, but not forming a straight line or right angle.

They are adjacent.

No indication of 90° or 180°, so not complementary or supplementary.

✔ Answer: Adjacent

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#### 6)
Two angles labeled ∠1 and ∠2, sharing a common vertex and side, and they appear to form a straight line.

So they are adjacent and supplementary.

But again, pick one.

Since they form a straight line, they are supplementary.

✔ Answer: Supplementary

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✔ Summary for Part 1:

| Problem | Relationship |
|--------|--------------|
| 1) | Adjacent |
| 2) | Supplementary |
| 3) | Vertical |
| 4) | Complementary |
| 5) | Adjacent |
| 6) | Supplementary |

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Part 2: Name the relationship: alternate interior, corresponding, or alternate exterior

These involve parallel lines cut by a transversal.

We’ll analyze each.

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#### 7)
Two parallel lines cut by a transversal. Angles labeled ∠1 and ∠2 are on opposite sides of the transversal, and inside the parallel lines.

This is alternate interior.

✔ Answer: Alternate interior

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#### 8)
Parallel lines cut by a transversal. ∠1 and ∠2 are on the same side of the transversal, and both inside the parallel lines.

That’s same-side interior, but that’s not one of the options.

Wait — options are: alternate interior, corresponding, or alternate exterior

So same-side interior is not listed.

But look: Are they on the same side? Yes.

Are they both inside? Yes.

But that’s consecutive interior — not among choices.

Wait — maybe I misread.

Wait — the angles are on opposite sides? Let me describe.

∠1 is above the top line, on the left side of the transversal.

∠2 is below the bottom line, on the right side of the transversal.

So they are on opposite sides of the transversal, and outside the parallel lines.

So they are alternate exterior angles.

✔ Answer: Alternate exterior

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#### 9)
Parallel lines cut by a transversal. ∠1 and ∠2 are on the same side of the transversal, and both are outside the parallel lines.

So they are corresponding angles?

Wait — corresponding angles are on the same side of the transversal and in the same relative position (e.g., both upper right).

Here, ∠1 is on the top right of the top line, ∠2 is on the bottom right of the bottom line.

So they are on the same side of the transversal (right), and both are above their respective lines? Wait — no.

Actually, ∠1 is above the top line, ∠2 is below the bottom line.

But both are on the right side of the transversal.

And both are outside the parallel lines.

So they are corresponding? No — corresponding would be like both upper right or both lower left.

But here, one is upper right, one is lower right — not corresponding.

Wait — are they alternate exterior?

Alternate exterior: on opposite sides of transversal and outside.

But here, both are on the same side of the transversal (right side), and outside.

So that’s corresponding? Not exactly.

Wait — actually, corresponding angles are defined as angles that are in the same relative position at each intersection.

So if ∠1 is the top-right angle at the top line, and ∠2 is the top-right angle at the bottom line, then they are corresponding.

But in this diagram, ∠2 is not the top-right — it’s the bottom-right.

Wait — let’s clarify.

If the transversal crosses the lines from top-left to bottom-right, then:

- At the top line: ∠1 is the upper right angle
- At the bottom line: ∠2 is the lower right angle

So they are on the same side of the transversal (right), and both are outside the parallel lines.

But are they corresponding?

Corresponding angles are: top-left with top-left, top-right with top-right, etc.

So ∠1 is top-right, and its corresponding angle would be the bottom-right angle — yes! That’s ∠2.

So ∠1 and ∠2 are corresponding angles.

✔ Answer: Corresponding

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#### 10)
Two parallel lines cut by a transversal. Angles labeled ∠1 and ∠2 are on opposite sides of the transversal, and inside the parallel lines.

So they are alternate interior angles.

✔ Answer: Alternate interior

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✔ Summary for Part 2:

| Problem | Relationship |
|--------|----------------------|
| 7) | Alternate interior |
| 8) | Alternate exterior |
| 9) | Corresponding |
| 10) | Alternate interior |

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✔ Final Answers:

Part 1:
1) Adjacent
2) Supplementary
3) Vertical
4) Complementary
5) Adjacent
6) Supplementary

Part 2:
7) Alternate interior
8) Alternate exterior
9) Corresponding
10) Alternate interior

Let me know if you'd like a visual explanation or help understanding any of the concepts!