5.1 polygon sum conjecture. angle exploration equilateral triangle 60°
TRANSCRIPT
![Page 1: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/1.jpg)
5.1 Polygon Sum Conjecture
![Page 2: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/2.jpg)
Angle Exploration
EquilateralTriangle60°
![Page 3: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/3.jpg)
Angle Exploration
Square90°
![Page 4: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/4.jpg)
Angle Exploration
RegularPentagon108°
![Page 5: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/5.jpg)
Angle Exploration
RegularHexagon120°
![Page 6: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/6.jpg)
Angle Exploration
RegularHeptagon129°
![Page 7: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/7.jpg)
Angle Exploration
RegularOctagon135°
![Page 8: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/8.jpg)
Angle Exploration
RegularNonagon140°
![Page 9: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/9.jpg)
Angle Exploration
RegularDecagon144°
![Page 10: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/10.jpg)
Angle Exploration
RegularDodecagon147°
![Page 11: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/11.jpg)
Angle Exploration• Summarize our
results
Sides Degrees3 60°4 90°5 108°6 120°7 129°8 135°9 140°
10 144°11 147°
Is there a correlation between the number of sides and the degrees?
![Page 12: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/12.jpg)
• What is the sum of the angles in each of the polygons
Angle Exploration
![Page 13: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/13.jpg)
Angle Exploration
• Summarize our results
Sides Total Degrees3 180° 60°4 360° 90°5 540° 108°6 720° 120°7 900° 129°8 1080° 135°9 1260° 140°
10 1440° 144°11 1620° 147°
Total Degrees in each polygon.
Do you see a pattern?
![Page 14: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/14.jpg)
Interior Angles in a Polygon
• The sum of the angles of the interior angles of a convex n-gon is (n-2)•180°
![Page 15: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/15.jpg)
Interior Angles in a Polygon
• What are the angle measures if the polygon is regular
• (n-2)•180°/n
![Page 16: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/16.jpg)
Sample Problems
![Page 17: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/17.jpg)
X=96
![Page 18: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/18.jpg)
X=85
![Page 19: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/19.jpg)
X=97
![Page 20: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/20.jpg)
X=117
![Page 21: 5.1 Polygon Sum Conjecture. Angle Exploration Equilateral Triangle 60°](https://reader035.vdocuments.net/reader035/viewer/2022062217/5697bfbb1a28abf838ca0c98/html5/thumbnails/21.jpg)
Exercise 12