Individual Task 5 (30.06.2020) - Sum of Interior Angles worksheet for calculating interior angles of polygons.

To solve this worksheet, we need to find the number of sides for each polygon and then calculate the sum of its interior angles.

---

✔ Key Formula:

The sum of the interior angles of a polygon with n sides is given by:

> Sum = (n – 2) × 180°

This formula works for any simple polygon (convex or concave), as long as it’s not self-intersecting.

---

Let’s go through each problem one by one.

---

## 🔹 Problem 1: Octagon (shown in image)
- Number of sides = 8
- Sum = (8 – 2) × 180° = 6 × 180° = 1080°

---

## 🔹 Problem 2: Pentagon (5-sided polygon)
- Number of sides = 5
- Sum = (5 – 2) × 180° = 3 × 180° = 540°

---

## 🔹 Problem 3: Quadrilateral (4-sided polygon)
- Number of sides = 4
- Sum = (4 – 2) × 180° = 2 × 180° = 360°

*(Note: Even though it’s an irregular quadrilateral, the formula still holds.)*

---

## 🔹 Problem 4: Triangle
- Number of sides = 3
- Sum = (3 – 2) × 180° = 1 × 180° = 180°

---

## 🔹 Problem 5: 12-gon
- Number of sides = 12
- Sum = (12 – 2) × 180° = 10 × 180° = 1800°

---

## 🔹 Problem 6: 17-gon
- Number of sides = 17
- Sum = (17 – 2) × 180° = 15 × 180° = 2700°

---

## 🔹 Problem 7: 18-gon
- Number of sides = 18
- Sum = (18 – 2) × 180° = 16 × 180° = 2880°

---

## 🔹 Problem 8: 14-gon
- Number of sides = 14
- Sum = (14 – 2) × 180° = 12 × 180° = 2160°

---

## ✍️ Final Answers:

| Problem | Number of Sides | Sum of Interior Angles |
|---------|------------------|--------------------------|
| 1 | 8 | 1080° |
| 2 | 5 | 540° |
| 3 | 4 | 360° |
| 4 | 3 | 180° |
| 5 | 12 | 1800° |
| 6 | 17 | 2700° |
| 7 | 18 | 2880° |
| 8 | 14 | 2160° |

---

✔ Summary: For any polygon, count the sides (n), plug into the formula `(n - 2) × 180°`, and you’ll get the total sum of interior angles. This is a fundamental concept in geometry!

Let me know if you’d like to see how the formula is derived!