Complementary & Supplementary Angles - Free Printable

Let's solve the problem step by step.

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Part 1: Circle the pairs of angles which are complementary or supplementary

#### Definitions:
- Complementary angles: Two angles that add up to 90°.
- Supplementary angles: Two angles that add up to 180°.

Now, check each pair:

1. 20° and 70° → 20 + 70 = 90° → ✔ Complementary
2. 70° and 120° → 70 + 120 = 190° → ✘
3. 80° and 100° → 80 + 100 = 180° → ✔ Supplementary
4. 50° and 40° → 50 + 40 = 90° → ✔ Complementary
5. 75° and 15° → 75 + 15 = 90° → ✔ Complementary
6. 80° and 90° → 80 + 90 = 170° → ✘
7. 20° and 170° → 20 + 170 = 190° → ✘
8. 30° and 140° → 30 + 140 = 170° → ✘
9. 30° and 70° → 30 + 70 = 100° → ✘
10. 35° and 65° → 35 + 65 = 100° → ✘

✔ Complementary pairs:
- 20° and 70°
- 50° and 40°
- 75° and 15°

✔ Supplementary pairs:
- 80° and 100°

> So, circle these three complementary pairs and one supplementary pair.

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Part 2: Calculate the missing angles

We'll go through each diagram.

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#### 1.
A straight line with a 60° angle shown. The other angle is adjacent to it, forming a straight line (180°).

So:
- Missing angle = 180° − 60° = 120°

✔ Answer: 120°

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#### 2.
A right triangle-like figure with a right angle (90°) and a 50° angle. The third angle is missing.

In a triangle, sum of angles = 180°.

So:
- Missing angle = 180° − 90° − 50° = 40°

✔ Answer: 40°

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#### 3.
Two angles at a point: one is 30°, and the total around a point is 360°, but this looks like two rays forming an angle with a straight line? Wait — let’s analyze.

Actually, the diagram shows a straight line with a 30° angle on one side, and a missing angle on the other side, possibly forming a straight line?

Wait — the figure shows a V-shape, with a 30° angle between the lines, and a right angle symbol? No — actually, in image description: "a V-shape with a 30° angle" and a curved angle marked.

Wait — looking at the standard layout: likely, it's a straight line split into two angles, one of which is 30°, and the other is unknown.

But if there's a right angle symbol, then it might be a right angle formed with another ray.

Wait — better interpretation:

Looking at common textbook diagrams:

- Diagram 3: A straight line, with a ray coming out from the middle, making a 30° angle on one side, and the other angle is missing. But wait — the angle shown is 30°, and the other part forms a straight line?

No — actually, it looks like a point with two rays forming a reflex angle, but more likely:

It's a straight line, and a ray divides it into two parts: one is 30°, the other is missing. Then:

- Missing angle = 180° − 30° = 150°

But wait — there’s a curved angle marked, so likely it's the larger angle.

Alternatively, perhaps it's a triangle or adjacent angles.

But based on typical problems:

If a straight line is divided into two angles, one is 30°, the other is 150°.

But the angle shown is 30°, and the missing one is opposite or adjacent?

Wait — the diagram shows a corner with a 30° angle, and a curved arc indicating the missing angle at the same vertex, likely forming a straight line.

So:

- The two angles form a straight line, so they are supplementary.

→ Missing angle = 180° − 30° = 150°

✔ Answer: 150°

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#### 4.
A straight line with a 108° angle marked. The missing angle is adjacent to it, forming a straight line.

So:
- Missing angle = 180° − 108° = 72°

✔ Answer: 72°

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#### 5.
This is a vertical line intersected by a horizontal line, forming four angles. One angle is 60°, and we need the missing angle.

At the intersection, vertical angles are equal, and adjacent angles are supplementary.

So:
- Adjacent angle to 60° = 180° − 60° = 120°
- Opposite angle = 60°
- Other adjacent = 120°

But the question says “calculate the missing angle” — likely the one adjacent to 60°, forming a straight line.

So:
→ 120°

✔ Answer: 120°

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#### 6.
Not visible — but likely a triangle or angle at a point.

Wait — no image, but based on common patterns.

Possibility: A triangle with two angles given? Or a straight line?

Since not described clearly, but assuming similar pattern.

But since the original says "calculate the following missing angles" and lists 8 items, but only 4 diagrams are shown, maybe some are missing.

Wait — in your message, only 4 diagrams are shown (1 to 4), but numbers go to 8.

Possibly the rest are missing.

But based on what’s provided:

Let me assume:

#### 7.
Likely a triangle with angles, or a point with multiple angles.

But without image, hard to tell.

But in many such worksheets:

- 7. Could be a triangle with two angles given? Or a reflex angle?

Wait — perhaps:

Let’s re-express:

Given the text:

> 5.
> 6.
> 7.
> 8.

But no images for 5–8.

Wait — in your initial message, only 4 diagrams are shown.

But you said "Calculate the following missing angles" and listed 1 to 8.

Possibly, the images are not fully uploaded.

But from what we have:

We can solve 1–4.

But let’s assume the rest are similar.

But based on common problems:

#### 5. Likely a straight line with a 60° angle — already solved as 120°.

Wait — diagram 1 already has 60° and asks for missing — answer 120°.

Then diagram 5 might be different.

But since images aren't clear, let's proceed with what we have.

But from the original:

Let me re-read:

You said:

> 1. [image with 60°]
> 2. [image with 50° and right angle]
> 3. [image with 30° and curved angle]
> 4. [image with 108°]

Then 5–8 are blank.

Possibly, the rest are not visible.

But maybe:

#### 5. A triangle with two angles known?

But without info, can’t solve.

Alternatively, perhaps:

Let’s suppose:

- 5. A triangle with angles 60°, 60°, missing → 60°? But no.

Wait — maybe the missing angles are:

But since only 4 diagrams are visible, I’ll solve those.

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✔ Final Answers:

#### Part 1: Complementary & Supplementary Pairs

Complementary (sum to 90°):
- 20° and 70°
- 50° and 40°
- 75° and 15°

Supplementary (sum to 180°):
- 80° and 100°

> Circle these.

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#### Part 2: Missing Angles

1. 120°
(180° − 60°)

2. 40°
(180° − 90° − 50° = 40°)

3. 150°
(180° − 30°)

4. 72°
(180° − 108°)

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If you can provide descriptions or images for questions 5–8, I can solve them too.

For now, here are the answers for the visible ones.

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✔ Summary:

Complementary pairs:
- 20° and 70°
- 50° and 40°
- 75° and 15°

Supplementary pair:
- 80° and 100°

Missing angles:
1. 120°
2. 40°
3. 150°
4. 72°

Let me know if you'd like help with 5–8!