To solve this problem, we need to find the sum of the interior angles for each polygon shown. The formula to calculate the sum of the interior angles of a polygon is:
Sum of interior angles = (n - 2) × 180°
where n is the number of sides of the polygon.
Let's go through each polygon one by one:
1.
First Polygon (Top Left):
- Number of sides (n) = 8
- Sum of interior angles = (8 - 2) × 180° = 6 × 180° = 1080°
2.
Second Polygon (Top Middle):
- Number of sides (n) = 5
- Sum of interior angles = (5 - 2) × 180° = 3 × 180° = 540°
3.
Third Polygon (Top Right):
- Number of sides (n) = 6
- Sum of interior angles = (6 - 2) × 180° = 4 × 180° = 720°
4.
Fourth Polygon (Middle Left):
- Number of sides (n) = 4
- Sum of interior angles = (4 - 2) × 180° = 2 × 180° = 360°
5.
Fifth Polygon (Middle Middle):
- Number of sides (n) = 8
- Sum of interior angles = (8 - 2) × 180° = 6 × 180° = 1080°
6.
Sixth Polygon (Middle Right):
- Number of sides (n) = 7
- Sum of interior angles = (7 - 2) × 180° = 5 × 180° = 900°
7.
Seventh Polygon (Bottom Left):
- Number of sides (n) = 9
- Sum of interior angles = (9 - 2) × 180° = 7 × 180° = 1260°
8.
Eighth Polygon (Bottom Middle):
- Number of sides (n) = 5
- Sum of interior angles = (5 - 2) × 180° = 3 × 180° = 540°
9.
Ninth Polygon (Bottom Right):
- Number of sides (n) = 3
- Sum of interior angles = (3 - 2) × 180° = 1 × 180° = 180°
Now, let's fill in the blanks for each polygon:
1. First Polygon: 8 sides, Sum = 1080°
2. Second Polygon: 5 sides, Sum = 540°
3. Third Polygon: 6 sides, Sum = 720°
4. Fourth Polygon: 4 sides, Sum = 360°
5. Fifth Polygon: 8 sides, Sum = 1080°
6. Sixth Polygon: 7 sides, Sum = 900°
7. Seventh Polygon: 9 sides, Sum = 1260°
8. Eighth Polygon: 5 sides, Sum = 540°
9. Ninth Polygon: 3 sides, Sum = 180°
Final Answer:
1. 8 sides, 1080°
2. 5 sides, 540°
3. 6 sides, 720°
4. 4 sides, 360°
5. 8 sides, 1080°
6. 7 sides, 900°
7. 9 sides, 1260°
8. 5 sides, 540°
9. 3 sides, 180°
Parent Tip: Review the logic above to help your child master the concept of interior angles of polygons worksheet.
