Working With Congruent Angles | 8th Grade Geometry Worksheets - Free Printable

Problem Overview:

The task involves working with congruent angles. There are two parts to the problem:

1. Part 1: Identify the congruent angle for each given angle.
2. Part 2: Draw a congruent angle for each given angle.

Let's solve each part step by step.

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Part 1: Circle the Congruent Angle for Each Given Angle

#### Step 1: Understand Congruent Angles
Two angles are congruent if they have the same measure. This means their shapes and sizes are identical, regardless of their orientation or position.

#### Step 2: Analyze Each Pair of Angles
We will compare the given angle in each row with the options provided (A) and (B) to determine which one is congruent.

##### Row 1:
- Given Angle: A right angle (90°).
- Option A: An acute angle (less than 90°).
- Option B: A right angle (90°).
- Conclusion: The congruent angle is (B).

##### Row 2:
- Given Angle: An acute angle.
- Option A: An acute angle with the same measure.
- Option B: A right angle (90°).
- Conclusion: The congruent angle is (A).

##### Row 3:
- Given Angle: An obtuse angle.
- Option A: An obtuse angle with the same measure.
- Option B: A right angle (90°).
- Conclusion: The congruent angle is (A).

##### Row 4:
- Given Angle: An acute angle.
- Option A: An acute angle with the same measure.
- Option B: A right angle (90°).
- Conclusion: The congruent angle is (A).

##### Row 5:
- Given Angle: An obtuse angle.
- Option A: An obtuse angle with the same measure.
- Option B: A right angle (90°).
- Conclusion: The congruent angle is (A).

#### Final Answers for Part 1:
1. Row 1: (B)
2. Row 2: (A)
3. Row 3: (A)
4. Row 4: (A)
5. Row 5: (A)

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Part 2: Draw a Congruent Angle for Each Given Angle

#### Step 1: Understand the Task
For each given angle measure, we need to draw an angle with the same measure. This involves using a protractor to ensure accuracy.

#### Step 2: Draw Each Angle
We will describe how to draw each angle using a protractor.

##### Angle (a): 60°
1. Draw a straight line segment.
2. Place the center of the protractor at one endpoint of the line segment.
3. Align the baseline of the protractor with the line segment.
4. Mark a point at the 60° mark on the protractor.
5. Draw a ray from the endpoint through the marked point.

##### Angle (b): 120°
1. Draw a straight line segment.
2. Place the center of the protractor at one endpoint of the line segment.
3. Align the baseline of the protractor with the line segment.
4. Mark a point at the 120° mark on the protractor.
5. Draw a ray from the endpoint through the marked point.

##### Angle (c): 30°
1. Draw a straight line segment.
2. Place the center of the protractor at one endpoint of the line segment.
3. Align the baseline of the protractor with the line segment.
4. Mark a point at the 30° mark on the protractor.
5. Draw a ray from the endpoint through the marked point.

##### Angle (d): 280°
1. Draw a straight line segment.
2. Place the center of the protractor at one endpoint of the line segment.
3. Align the baseline of the protractor with the line segment.
4. Mark a point at the 280° mark on the protractor.
5. Draw a ray from the endpoint through the marked point.

#### Final Answer for Part 2:
- Draw each angle as described above using a protractor to ensure accuracy.

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Final Answer:

\[
\boxed{
\text{Part 1: (B), (A), (A), (A), (A)} \\
\text{Part 2: Draw each angle using a protractor as described.}
}
\]