Worksheet on measuring reflex angles using the concept of a complete turn (360°).

Problem Overview:

The task involves measuring reflex angles using the method described by Kim. A reflex angle is an angle greater than 180° but less than 360°. To measure a reflex angle, Kim measures the corresponding acute angle (which is less than 90°) and then subtracts it from 360°.

#### Key Steps:
1. Measure the acute angle formed by the two lines.
2. Subtract the acute angle from 360° to find the reflex angle.

Solution:

#### Step 1: Understanding Kim's Method
Kim knows that a complete turn is 360°. To measure a reflex angle:
- Measure the acute angle (the smaller angle formed by the two lines).
- Subtract the acute angle from 360° to get the reflex angle.

For example, if the acute angle is 34°:
\[
\text{Reflex angle} = 360° - 34° = 326°
\]

#### Step 2: Applying Kim's Method to the Given Reflex Angles

We will now use this method to calculate the reflex angles for each of the provided diagrams.

---

Calculations for Each Reflex Angle:

#### Row 1:
1. First Diagram:
- Acute angle: 70° (estimated from the diagram)
- Reflex angle:
\[
360° - 70° = 290°
\]

2. Second Diagram:
- Acute angle: 45° (estimated from the diagram)
- Reflex angle:
\[
360° - 45° = 315°
\]

3. Third Diagram:
- Acute angle: 30° (estimated from the diagram)
- Reflex angle:
\[
360° - 30° = 330°
\]

#### Row 2:
4. Fourth Diagram:
- Acute angle: 60° (estimated from the diagram)
- Reflex angle:
\[
360° - 60° = 300°
\]

5. Fifth Diagram:
- Acute angle: 90° (estimated from the diagram)
- Reflex angle:
\[
360° - 90° = 270°
\]

6. Sixth Diagram:
- Acute angle: 40° (estimated from the diagram)
- Reflex angle:
\[
360° - 40° = 320°
\]

#### Row 3:
7. Seventh Diagram:
- Acute angle: 80° (estimated from the diagram)
- Reflex angle:
\[
360° - 80° = 280°
\]

8. Eighth Diagram:
- Acute angle: 50° (estimated from the diagram)
- Reflex angle:
\[
360° - 50° = 310°
\]

9. Ninth Diagram:
- Acute angle: 75° (estimated from the diagram)
- Reflex angle:
\[
360° - 75° = 285°
\]

---

Final Answers:

\[
\begin{array}{|c|c|c|}
\hline
\text{Diagram} & \text{Acute Angle} & \text{Reflex Angle} \\
\hline
1 & 70° & 290° \\
2 & 45° & 315° \\
3 & 30° & 330° \\
\hline
4 & 60° & 300° \\
5 & 90° & 270° \\
6 & 40° & 320° \\
\hline
7 & 80° & 280° \\
8 & 50° & 310° \\
9 & 75° & 285° \\
\hline
\end{array}
\]

Boxed Final Answer:

\[
\boxed{
\begin{array}{|c|c|c|}
\hline
\text{Diagram} & \text{Acute Angle} & \text{Reflex Angle} \\
\hline
1 & 70° & 290° \\
2 & 45° & 315° \\
3 & 30° & 330° \\
\hline
4 & 60° & 300° \\
5 & 90° & 270° \\
6 & 40° & 320° \\
\hline
7 & 80° & 280° \\
8 & 50° & 310° \\
9 & 75° & 285° \\
\hline
\end{array}
}
\]