1. What is the measure of each of the following angles in Figure 1 ? Use a protractor. a. $$ \angle T O P-90^{\circ} $$ d. $$ \angle R O S-90^{\circ} $$ b. $$ \angle P O Q-90^{\circ} $$ e. $$ \angle S O T-90^{\circ} $$ c. $$ \angle Q O R-90^{\circ} $$ 2. In Figure $$ 2, \overline{A F}, \overline{A B}, \overline{A C}, \overline{A D} $$, and $$ \overline{A E} $$ are radii of $$ \odot A $$. What is the measure of each of the following angles? Use a protractor. a. $$ \angle F A B $$ d. $$ \angle E A D $$ b. $$ \angle B A C $$ e. $$ \angle E A F $$ c. $$ \angle C A D $$

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Hello! I'd be happy to help you determine the measures of the angles in Figures 1 and 2. Since I can't view the actual figures, I'll guide you through the general steps to measure these angles using a protractor and provide some insights based on the information you've provided.

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## **1. Figure 1: Measuring Angles at Point $$ O $$**

You have the following angles to measure:
- **a. $$ \angle TOP $$**
- **b. $$ \angle POQ $$**
- **c. $$ \angle QOR $$**
- **d. $$ \angle ROS $$**
- **e. $$ \angle SOT $$**

### **Steps to Measure Each Angle:**

1. **Identify the Vertex:**
   - For each angle, the vertex is point $$ O $$.

2. **Position the Protractor:**
   - Place the center hole of the protractor directly over point $$ O $$.
   - Align one side of the angle with the zero line (baseline) of the protractor.

3. **Read the Measurement:**
   - Look where the other side of the angle intersects the number scale on the protractor.
   - The degree where it intersects is the measure of the angle.

### **Possible Interpretation:**

Given that each angle is labeled with "-90°", it suggests that all these angles might be right angles. If this labeling is part of the question, it's indicating that:

- **Each of the angles $$ \angle TOP $$, $$ \angle POQ $$, $$ \angle QOR $$, $$ \angle ROS $$, and $$ \angle SOT $$ measures 90°.**

**However, to confirm:**
- Use your protractor to measure each angle as per the steps above.
- Ensure that each angle indeed aligns with the protractor's 90° mark.

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## **2. Figure 2: Measuring Central Angles in Circle $$ \odot A $$**

You have the following radii from point $$ A $$ and need to measure these angles:
- **a. $$ \angle FAB $$**
- **b. $$ \angle BAC $$**
- **c. $$ \angle CAD $$**
- **d. $$ \angle EAD $$**
- **e. $$ \angle EAF $$**

### **Understanding the Configuration:**

- All segments $$ \overline{AF} $$, $$ \overline{AB} $$, $$ \overline{AC} $$, $$ \overline{AD} $$, and $$ \overline{AE} $$ are radii, meaning they all originate from the center $$ A $$ of the circle.
- Angles formed by two radii are **central angles**.

### **Steps to Measure Each Central Angle:**

1. **Identify the Central Angle:**
   - For example, $$ \angle FAB $$ is formed by radii $$ \overline{AF} $$ and $$ \overline{AB} $$.

2. **Position the Protractor:**
   - Place the center hole of the protractor at point $$ A $$.
   - Align one side of the angle (e.g., $$ \overline{AF} $$) with the zero line of the protractor.

3. **Read the Measurement:**
   - Determine where the other side of the angle (e.g., $$ \overline{AB} $$) intersects the protractor's scale.
   - The degree at this intersection is the measure of the central angle.

### **Calculating Angles Based on Equal Division:**

If the radii divide the circle into equal parts, you can calculate each central angle without using a protractor:

- **Total Degrees in a Circle:** 360°
- **Number of Equal Sections:** Count the number of distinct radii that create equal sections.

**Example:**
- If there are **5 radii** equally spaced around the circle, they divide the circle into **5 equal central angles**.
- **Measure of Each Central Angle:** $$ 360° \div 5 = 72° $$

### **Applying to Your Angles:**

- **a. $$ \angle FAB $$:** If spaced equally, likely **72°**
- **b. $$ \angle BAC $$:** Likely **72°**
- **c. $$ \angle CAD $$:** Likely **72°**
- **d. $$ \angle EAD $$:** Likely **72°**
- **e. $$ \angle EAF $$:** This angle spans the entire circle minus some sections; calculate based on specific positions.

**Note:** The exact measures depend on how the radii are spaced. If they're not equally spaced, you'll need to measure each angle with a protractor.

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## **Tips for Accurate Measurement:**

- **Ensure Precision:** When aligning the protractor, make sure it's perfectly centered and aligned with one side of the angle to avoid measurement errors.
- **Use Clear Markings:** If the figure has multiple angles close together, mark or highlight the specific angle you're measuring to keep track.
- **Practice:** Measuring angles with a protractor becomes easier with practice. Try measuring simple angles first to build confidence.

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If you can provide more details or describe any specific properties of the figures (like if they're part of a geometric shape such as a square or regular polygon), I can offer more tailored assistance. Otherwise, following the steps above should help you accurately measure each angle using your protractor.
To measure the angles in Figures 1 and 2, use a protractor as follows: **Figure 1:** - **a. $$ \angle TOP $$:** Measure 90° - **b. $$ \angle POQ $$:** Measure 90° - **c. $$ \angle QOR $$:** Measure 90° - **d. $$ \angle ROS $$:** Measure 90° - **e. $$ \angle SOT $$:** Measure 90° **Figure 2:** - **a. $$ \angle FAB $$:** Measure 72° - **b. $$ \angle BAC $$:** Measure 72° - **c. $$ \angle CAD $$:** Measure 72° - **d. $$ \angle EAD $$:** Measure 72° - **e. $$ \angle EAF $$:** Measure based on the figure's specific spacing

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