Maths 5 week exam

Polygons

Sum of the interior angles in a polygon with n sides

= 180(n-2)

e.g

calculate the sum of the interior angles in a shape whith 25 sides

=180(25-2)

=180x23

=4140 degrees

One interior angle in a 25 sided shape 

= 165.6 degrees (4140 degrees divided by 25)

Exterior Angles

Sum of the exterior angles in any polygon 

=360 degrees

Interior angles and Exterior angles always add up to

=180 degrees

Tessalations

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.

Expanding Brakets

complex exalmples of expanding brakets

e.g 3x squared (2x squared + 7x - 4)

= 6x by the power of 4