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1. Learning Objectives
- Derive the formula for the sum of interior angles of an n-sided polygon.
- Calculate the total interior angle sum for any convex polygon.
- Find the number of sides (n) when the angle sum is known.
2. Key Notes
The sum of interior angles depends on the number of triangles that can be formed from one vertex of the polygon.
Sum of Interior Angles (S) = (n - 2) × 180°
Where n is the number of sides of the polygon.
- Triangle (n=3): (3-2)×180 = 180°
- Quadrilateral (n=4): (4-2)×180 = 360°
- Pentagon (n=5): (5-2)×180 = 540°
Click the button below each question to reveal the explanation.
1. Find the sum of interior angles of a hexagon (6 sides).
Use formula: (6 - 2) × 180° = 4 × 180° = 720°. Ans: 720°
2. What is the sum of interior angles of an octagon (8 sides)?
(8 - 2) × 180° = 6 × 180° = 1080°. Ans: 1080°
3. If a polygon has 12 sides, what is its interior angle sum?
(12 - 2) × 180° = 10 × 180° = 1800°. Ans: 1800°
4. Find the sum of interior angles for a polygon with 20 sides.
(20 - 2) × 180° = 18 × 180° = 3240°. Ans: 3240°
5. If the sum of interior angles is 900°, how many sides does it have?
900 = (n - 2) × 180 → 900/180 = n - 2 → 5 = n - 2 → n = 7. Ans: 7 sides (Heptagon)
6. A polygon has an interior angle sum of 1440°. Find n.
1440/180 = n - 2 → 8 = n - 2 → n = 10. Ans: 10 sides (Decagon)
7. How many triangles are formed from one vertex in a nonagon (9 sides)?
The number of triangles is (n - 2). 9 - 2 = 7. Ans: 7 triangles
8. What is the sum of interior angles of a quadrilateral?
(4 - 2) × 180° = 360°. Ans: 360°
9. If n = 15, calculate the total interior sum.
(15 - 2) × 180 = 13 × 180 = 2340°. Ans: 2340°
10. Find the number of sides if the sum is 2160°.
2160 / 180 = 12. n - 2 = 12 → n = 14. Ans: 14 sides
11. A regular polygon has 5 sides. Sum of angles?
(5 - 2) × 180° = 540°. Ans: 540°
12. True or False: Sum of interior angles increases as sides increase.
Correct, the formula is directly proportional to n. Ans: True
13. Find the sum for an 11-sided polygon (Hendecagon).
(11 - 2) × 180 = 9 × 180 = 1620°. Ans: 1620°
14. If n = 100, what is the interior sum?
98 × 180 = 17640°. Ans: 17640°
15. What polygon has an interior sum of 180°?
(n - 2) × 180 = 180 → n - 2 = 1 → n = 3. Ans: Triangle
16. Calculate n if sum = 3600°.
3600 / 180 = 20. n - 2 = 20 → n = 22. Ans: 22 sides
17. Sum of angles of a 13-sided polygon?
11 × 180 = 1980°. Ans: 1980°
18. If a polygon is split into 4 triangles, how many sides does it have?
Triangles = n - 2. 4 = n - 2 → n = 6. Ans: 6 sides
19. Sum of angles for a dodecagon (12 sides)?
10 × 180 = 1800°. Ans: 1800°
20. Can a polygon have an interior sum of 500°?
No, the sum must be a multiple of 180°. 500/180 is not an integer. Ans: No