Complementary and Supplementary Angles Worksheets - Free Printable

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Let me help you solve and explain each problem step-by-step based on the description of what's typically found in such worksheets.

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Problem 1: Complementary & Supplementary Angles

#### Part A: Name a pair of acute complementary angles
- Complementary angles are two angles whose measures add up to 90°.
- Acute angles are angles less than 90°.
- So we're looking for two angles that:
- Are both less than 90°
- Add up to 90°

From the diagram (which likely shows intersecting lines forming four angles around a point), if there’s a right angle marked (90°), then the two adjacent angles forming that right angle would be complementary.

Example answer:
If ∠A and ∠B form a right angle together, then ∠A and ∠B are a pair of acute complementary angles.

> ✔ Answer: ∠A and ∠B (or whatever labels are used in your diagram)

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#### Part B: Find the measure of the angle that is complementary to ∠ABC

This means:
We need to find an angle that, when added to ∠ABC, equals 90°.

So:
$$
\text{Complement of } \angle ABC = 90^\circ - \angle ABC
$$

But since we don’t have the measure of ∠ABC, let’s assume from common problems that maybe ∠ABC is given as, say, 35°.

Then:
$$
90^\circ - 35^\circ = 55^\circ
$$

> ✔ Answer: 55° (if ∠ABC = 35°)

But without the actual value, this depends on the diagram.

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#### Part C: Name the angle adjacent to ∠BDC

- Adjacent angles share a common vertex and a common side but do not overlap.
- So look at ∠BDC — it has vertex D, and sides DB and DC.
- The adjacent angle would be one that shares side DB or DC and vertex D.

For example, if there’s another angle like ∠CDA or ∠BDF, depending on labeling.

> ✔ Answer: Likely ∠ADC or ∠BDA, depending on the diagram.

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Problem 2: Supplementary Angles

#### Part A: Name any pair of adjacent angles

- Adjacent angles share a common side and vertex.
- In a typical diagram with two intersecting lines or rays, such as a straight line with a ray coming out, adjacent angles might be like ∠1 and ∠2 if they are next to each other.

> ✔ Example: ∠1 and ∠2 (based on labels in diagram)

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#### Part B: Find m∠DBC

Again, we need more info. But suppose ∠DBC is part of a straight line (180°), and another angle is given.

For example, if ∠DBA = 120°, and points A, B, C are colinear, then:

$$
m\angle DBC = 180^\circ - 120^\circ = 60^\circ
$$

> ✔ Answer: 60° (if ∠DBA = 120°)

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#### Part C: Determine the complement of 52°

- Complement = $ 90^\circ - 52^\circ = 38^\circ $

> ✔ Answer: 38°

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#### Part D: Name the angle that forms a linear pair with ∠XYZ

- A linear pair consists of two adjacent angles whose non-common sides form a straight line → sum to 180°.
- So the angle forming a linear pair with ∠XYZ must be adjacent and on a straight line.

> ✔ Answer: Likely ∠XYW or ∠XZY, depending on diagram.

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✔ Final Summary (General Answers):

| Question | Answer |
|--------|--------|
| 1a. Pair of acute complementary angles | ∠A and ∠B (example) |
| 1b. Complement of ∠ABC | $90^\circ - \angle ABC$ (e.g., 55° if ∠ABC = 35°) |
| 1c. Angle adjacent to ∠BDC | ∠ADC or ∠BDA (depends on diagram) |
| 2a. Pair of adjacent angles | ∠1 and ∠2 |
| 2b. m∠DBC | Depends on diagram (e.g., 60°) |
| 2c. Complement of 52° | 38° |
| 2d. Linear pair with ∠XYZ | ∠XYW (adjacent angle forming straight line) |

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🔍 How to Solve These Problems:

1. Look for right angles (90°) → complementary pairs.
2. Look for straight lines (180°) → supplementary pairs.
3. Adjacent angles → share a side and vertex.
4. Linear pairs → adjacent angles forming a straight line → sum to 180°.
5. Complement = 90° − angle
Supplement = 180° − angle

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👉 If you can describe the diagram (e.g., “two lines intersecting at point O”, “ray BD splits angle ABC into two parts”, etc.), I can give exact answers based on the labels and values.

Let me know!