median
don steward
mathematics teaching 10 ~ 16

## Tuesday, 22 December 2015

### angles in tessellations

regular pentagons with rhombuses

what are the angles in the rhombuses?

regular pentagons with isosceles triangles

what are the angles in the isosceles triangles?

regular octagons with star octagons

what are the angles in the star octagons?

regular heptagons with 'bow-tie' octagons

what are the angles in the bow-tie?

show that a + b = 240 degrees
and 2a + b = 360 degrees

hence deduce the sizes of angle 'a' and angle 'b'

what is the relationship between angle 'a'
and angle 'b' ?

what is the relationship between angle 'b'
and angle 'a' ?

what is the relationship between angle 'c'
and angle 'a' ?

give reasons why c = 135

find a relationship between 'a' and 'b'

find a relationship between 'a' and 'd'

hence work out all of the angles in the pentagons

tessellation of pentagons discovered by:
Casey Mann
Jennifer McLoud
David von Deran

(University of Washington Bothell)

August 2015