Relationship of Angles Worksheet for 4th - 7th Grade | Lesson Planet - Free Printable

It looks like you've uploaded a worksheet titled "Identify Complementary or Supplementary Angles" that asks students to determine whether angles 1 and 2 in each figure are complementary (sum to 90°) or supplementary (sum to 180°).

Since I can't view images directly, I'll guide you through how to solve this type of problem based on the typical structure of such worksheets. Below is a general explanation and solution method for each type of diagram you might find.

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🔍 Step-by-Step Guide to Solving the Problem

#### ✔ Definitions:
- Complementary angles: Two angles whose measures add up to 90°.
- Supplementary angles: Two angles whose measures add up to 180°.

You’ll need to analyze each diagram and determine the relationship between ∠1 and ∠2.

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📐 Common Diagram Types (and How to Analyze Them)

Let’s assume the worksheet has 6 diagrams labeled A–F. Here's how to interpret each:

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#### Diagram A: Right Triangle
- Shows a right triangle with one angle marked as 90°.
- ∠1 and ∠2 are the two acute angles.
- In any triangle, the sum of angles = 180°.
- Since one angle is 90°, the other two must add to 90° → complementary.

✔ Answer: Complementary

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#### Diagram B: Intersecting Lines
- Two lines intersect, forming four angles.
- ∠1 and ∠2 are adjacent angles that form a straight line (a linear pair).
- Linear pairs always sum to 180° → supplementary.

✔ Answer: Supplementary

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#### Diagram C: Perpendicular Lines
- Lines intersect at 90° (right angle symbol shown).
- ∠1 and ∠2 are both parts of a right angle.
- If they are adjacent and make up the 90° angle, their sum is 90° → complementary.

✔ Answer: Complementary

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#### Diagram D: Adjacent Angles on a Straight Line
- ∠1 and ∠2 are next to each other and form a straight line.
- This means they are a linear pair, so they add to 180° → supplementary.

✔ Answer: Supplementary

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#### Diagram E: Vertical Angles
- ∠1 and ∠2 are vertical angles (opposite angles formed by two intersecting lines).
- Vertical angles are equal, but unless they are both 90°, they aren’t necessarily complementary or supplementary.
- However, if they are part of a straight line or right angle, we check accordingly.
- But usually, if they’re just opposite angles, they are not necessarily complementary or supplementary — unless more info is given.

⚠️ But in most such worksheets, if ∠1 and ∠2 are vertical angles and the figure shows a right angle, then they may be 90° each → complementary? No! Because 90 + 90 = 180 → supplementary.

Wait: 90° + 90° = 180° → supplementary.

But only if they're adjacent and form a straight line.

If ∠1 and ∠2 are vertical angles and both are 45°, then 45 + 45 = 90 → complementary.

So it depends on the actual measure.

But since no numbers are given, we look at geometry.

👉 Usually, if two angles are vertical angles, they are equal, but unless they are both 90°, they don't sum to 90° or 180°.

So unless they are part of a right angle or straight line, they are neither.

But in many cases, if they are vertical angles formed by perpendicular lines, they are all 90° → so 90° + 90° = 180° → supplementary?

Wait: no — two angles are supplementary if they add to 180°, regardless of position.

But if ∠1 and ∠2 are both 90°, then yes, they are supplementary.

But are they adjacent? No — vertical angles are not adjacent.

So even if both are 90°, they are not adjacent, so they don’t form a linear pair.

But the definition of supplementary doesn't require adjacency — just that the sum is 180°.

So if ∠1 = 90° and ∠2 = 90°, then they are supplementary.

Similarly, if both are 45°, they are complementary.

But without labels, we rely on visual cues.

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#### Common Case: Perpendicular Lines (Right Angle Symbol)

If the lines are perpendicular (right angle symbol), then all angles are 90°.

So if ∠1 and ∠2 are any two angles in such a figure, and they are not adjacent, but just labeled, we still ask: do they add to 90° or 180°?

- If both are 90° → 90 + 90 = 180 → supplementary
- If one is 90° and the other is 90° → same
- But if they are adjacent and form a corner, maybe they are parts of 90°

Wait — let’s clarify.

In a standard perpendicular intersection:

- All four angles are 90°.
- So any two adjacent angles: 90° + 90° = 180° → supplementary
- Any two opposite (vertical): 90° + 90° = 180° → also supplementary

So all pairs of angles here are supplementary.

But wait: complementary means sum to 90° — so two 45° angles would be complementary.

But in a perpendicular intersection, all angles are 90° → so no two angles add to 90° unless one is 0°, which isn’t possible.

So in such a case, no two angles are complementary — but all pairs are supplementary.

So if ∠1 and ∠2 are any two angles from perpendicular lines, and both are 90°, then:

✔ Answer: Supplementary

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#### Diagram F: Transversal and Parallel Lines
- Might show parallel lines cut by a transversal.
- ∠1 and ∠2 could be:
- Alternate interior → equal
- Corresponding → equal
- Consecutive interior → supplementary (add to 180°)
- Or adjacent angles forming a straight line → supplementary

So if ∠1 and ∠2 are consecutive interior angles, they are supplementary.

If they are acute and obtuse on the same side of the transversal → supplementary.

If they are same-side interior angles, then supplementary.

So likely: ✔ Supplementary

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✔ Final Answers (Typical Worksheet Pattern):

| Diagram | Relationship |
|--------|--------------|
| A | Complementary (acute angles in right triangle) |
| B | Supplementary (linear pair) |
| C | Complementary (form 90° angle) |
| D | Supplementary (linear pair) |
| E | Supplementary (if both 90°, or vertical angles in perpendicular lines) |
| F | Supplementary (same-side interior angles) |

> ⚠️ Note: The exact answer depends on the diagram. But these are common setups.

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✔ Summary of How to Solve:

1. Look at the diagram and identify:
- Are the angles adjacent?
- Do they form a straight line? → Then supplementary
- Do they form a right angle? → Then complementary
- Are they vertical angles? → Equal, but check sum
- Is there a right angle symbol? → Indicates 90°
- Are lines parallel? → Use properties of transversals

2. Add the angles mentally (or use known facts):
- If they make a straight line → 180° → supplementary
- If they make a right angle → 90° → complementary

3. Label your answer as either Complementary or Supplementary

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📝 Example Answer Format (for the worksheet):

```
A: Complementary
B: Supplementary
C: Complementary
D: Supplementary
E: Supplementary
F: Supplementary
```

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If you can describe each diagram (e.g., "Diagram A: a right triangle with angles labeled"), I can give you the exact answers.

Alternatively, if you can paste a text description of the figures, I’ll solve them step by step!