© T Madas. Equilateral Triangle Square Pentagon Hexagon Heptagon Octagon Enneagon Decagon...
-
Upload
lynette-briggs -
Category
Documents
-
view
229 -
download
2
Transcript of © T Madas. Equilateral Triangle Square Pentagon Hexagon Heptagon Octagon Enneagon Decagon...
© T Madas
EquilateralTriangle
SquarePentagon Hexagon
Heptagon Octagon Enneagon
Decagon Hendecagon Dodecagon
© T Madas
Interior Angle
What is the sum of the interior angles of this enneagon?
7 x 180° =1260°
A 9–sided polygon is split into 7 triangles
© T Madas
What is the sum of the interior angles of this enneagon?What is the sum of the interior angles of a polygon with n sides?
A n - sided polygon can be split into triangles
n – 2
( 2)n - 180´ ° 180( 2)n= -=sum
© T Madas
sum of the interior angles of various polygons
triangle180°
quadrilateral180° x 2= 360°
pentagon180° x 3= 540°
hexagon180° x 4= 720°
heptagon180° x 5= 900°
octagon180° x 6= 1080°
© T Madas
Consider the following polygon
What do the exterior angles of a polygon add up to?
Exterior Angle
© T Madas
Exterior Angle
Consider the following polygon
What do the exterior angles of a polygon add up to?
© T Madas
Central Angle
Central Angle
The central angle of a regular polygon
How do we find the central angle of a regular polygon with n sides?
Central angle =360°
n
© T Madas
The central angle of a regular polygon
How do we find the central angle of a regular polygon with n sides?
Central angle of a pentagon =
360°5
= 72°
© T Madas
The central angle of a regular polygon
How do we find the central angle of a regular polygon with n sides?
Central angle of an octagon =
360°8
= 45°
© T Madas
The exterior angle of a regular pentagon
exterior angle =360°5
The exterior angles of any polygon add up to
360°
= 72°
© T Madas
The exterior angle of a regular octagon
exterior angle = 360°8
= 45°
The exterior angles of any polygon add up to
360°
© T Madas
The interior angle of a regular polygon
A n - sided polygon can be split into triangles
n – 2
( 2)n - 180´ ° 180( 2)n= -=sum
Interior angle =180(n – 2)
n
© T Madas
the interior angles of various regular polygons
equilateraltriangle180°
square180° x 2= 360°
pentagon180° x 3= 540°
hexagon
180° x 4= 720°heptagon
180° x 5= 900°
octagon180° x 6= 1080°
÷ 3= 60° 360°÷ 4= 90° 540°÷ 5= 72°
720°÷ 6= 120° 900°÷ 7≈ 128.6° 1080°÷ 8= 135°
© T Madas
central angle =360°
n
exterior angle =360°n
For every regular polygon
interior angle =180(n – 2)
n
These formulae are very easy to derive