Sum of the interior angles in a polygon with n sides
calculate the sum of the interior angles in a shape whith 25 sides
One interior angle in a 25 sided shape
= 165.6 degrees (4140 degrees divided by 25)
Sum of the exterior angles in any polygon
Interior angles and Exterior angles always add up to
In each angle in a regular shape that tessalates each interior angle is a factor of 360
All quadrilaterals (including iregular ones) tessalate because all of the interior angles add up to 360 degrees so they will always tessalate.
Triangle - each angle is 120 degrees. 120 is a factor of 360. Therefore, regular triangles tessalate.
Pentagon - each angle is 72 degrees. 72 is a factor of 360. Therefore, regular pentagons tessalate.
Hexagon - each angle is 60 degrees. 60 is a factor of 360. Therefore, all regular pentagons tessalate.
Heptagon - each angle is 51 degrees. 51 does not go perfectly into 360. Therefore, all regular heptagons do not tessalate.
Pentagon - each angle is 45 degrees. 45 is a factor of 360. Therefore, all regular pentagons tessalate.
complex exalmples of expanding brakets
e.g 3x squared (2x squared + 7x - 4)
= 6x by the power of 4