Finding the Sum of a Polygon’s Interior Angles 5-Oct-15 Here are some polygons The word...
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![Page 1: Finding the Sum of a Polygon’s Interior Angles 5-Oct-15 Here are some polygons The word ‘polygon’ is a Greek word. Poly gon Poly means many and gon means.](https://reader036.fdocuments.us/reader036/viewer/2022082710/56649e865503460f94b8a206/html5/thumbnails/1.jpg)
Finding the Sum of a Polygon’s Interior
Angles
Apr 19, 2023
Here are some polygons
The word ‘polygon’ is
a Greek word.
PolyPoly means many
and gongon means angles.
Triangle
Pentagon
Octagon
![Page 2: Finding the Sum of a Polygon’s Interior Angles 5-Oct-15 Here are some polygons The word ‘polygon’ is a Greek word. Poly gon Poly means many and gon means.](https://reader036.fdocuments.us/reader036/viewer/2022082710/56649e865503460f94b8a206/html5/thumbnails/2.jpg)
a
b
c
ed
How to find the sum of the interior angles – i.e. How to find a + b + c + d + e
![Page 3: Finding the Sum of a Polygon’s Interior Angles 5-Oct-15 Here are some polygons The word ‘polygon’ is a Greek word. Poly gon Poly means many and gon means.](https://reader036.fdocuments.us/reader036/viewer/2022082710/56649e865503460f94b8a206/html5/thumbnails/3.jpg)
How to find the sum of the interior angles – i.e. How to find a + b + c + d + e
Split the shape up into triangles
![Page 4: Finding the Sum of a Polygon’s Interior Angles 5-Oct-15 Here are some polygons The word ‘polygon’ is a Greek word. Poly gon Poly means many and gon means.](https://reader036.fdocuments.us/reader036/viewer/2022082710/56649e865503460f94b8a206/html5/thumbnails/4.jpg)
How to find the sum of the interior angles – i.e. How to find a + b + c + d + e
Split the shape up into triangles
Each triangle contains 1800
18001800
1800
![Page 5: Finding the Sum of a Polygon’s Interior Angles 5-Oct-15 Here are some polygons The word ‘polygon’ is a Greek word. Poly gon Poly means many and gon means.](https://reader036.fdocuments.us/reader036/viewer/2022082710/56649e865503460f94b8a206/html5/thumbnails/5.jpg)
How to find the sum of the interior angles – i.e. How to find a + b + c + d + e
Split the shape up into triangles
Each triangle contains 1800
3 x 180 = 54001800
1800
1800
![Page 6: Finding the Sum of a Polygon’s Interior Angles 5-Oct-15 Here are some polygons The word ‘polygon’ is a Greek word. Poly gon Poly means many and gon means.](https://reader036.fdocuments.us/reader036/viewer/2022082710/56649e865503460f94b8a206/html5/thumbnails/6.jpg)
How to find the sum of the interior angles – i.e. How to find a + b + c + d + e
Split the shape up into triangles
Each triangle contains 1800
3 x 180 = 5400
The sum of the interior angles is 5400
18001800
1800
![Page 7: Finding the Sum of a Polygon’s Interior Angles 5-Oct-15 Here are some polygons The word ‘polygon’ is a Greek word. Poly gon Poly means many and gon means.](https://reader036.fdocuments.us/reader036/viewer/2022082710/56649e865503460f94b8a206/html5/thumbnails/7.jpg)
Name Number of Sides
Sum of Interior Angles
Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
Copy and complete this table. Find the interior angles by drawing and splitting up into triangles.
![Page 8: Finding the Sum of a Polygon’s Interior Angles 5-Oct-15 Here are some polygons The word ‘polygon’ is a Greek word. Poly gon Poly means many and gon means.](https://reader036.fdocuments.us/reader036/viewer/2022082710/56649e865503460f94b8a206/html5/thumbnails/8.jpg)
Name Number of Sides
Sum of Interior Angles
Quadrilateral 4 360
Pentagon 5 540
Hexagon 6 720
Heptagon 7 900
Octagon 8 1080
Nonagon 9 1260
Decagon 10 1440
Copy and complete this table. Find the interior angles by drawing and splitting up into triangles.
![Page 9: Finding the Sum of a Polygon’s Interior Angles 5-Oct-15 Here are some polygons The word ‘polygon’ is a Greek word. Poly gon Poly means many and gon means.](https://reader036.fdocuments.us/reader036/viewer/2022082710/56649e865503460f94b8a206/html5/thumbnails/9.jpg)
1200
Interior Angle
NB. If the polygon is regular, to find an interior angle use the rule:
Int.Angle = 180 – (360 ÷ n)
n is the number of sides
Int. = 180 – (360 ÷ 6) 180 – 60 =120
Regular Polygons
![Page 10: Finding the Sum of a Polygon’s Interior Angles 5-Oct-15 Here are some polygons The word ‘polygon’ is a Greek word. Poly gon Poly means many and gon means.](https://reader036.fdocuments.us/reader036/viewer/2022082710/56649e865503460f94b8a206/html5/thumbnails/10.jpg)
1200
Interior Angle
NB. If the polygon is regular, to find an exterior angle use the rule:
Ext.Angle = 360 ÷ n
n is the number of sides
And Ext. Angle = 180 – Int.Angle
Regular Polygons
exterior angle (180 – 120 = 60