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LOGO Challenge 5 - Patch

Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?

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LOGO Challenge 6 - Triangles and Stars

Recreating the designs in this challenge requires you to break a problem down into manageable chunks and use the relationships between triangles and hexagons. An exercise in detail and elegance.

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Sharks Are Symmetric

Weekly Problem 35 - 2012
How many more triangles need to be shaded to make the pattern have a line of symmetry?

Angle of Overlap

Stage: 3 Short Challenge Level: Challenge Level:1

$\angle CBE = (180-75-60)^{\circ} = 45 ^{\circ}$
$\angle DEB= (180-65-60)^{\circ}= 55 ^{\circ}$
$\angle GHB= (45+55)^{\circ} = 100^{\circ}$ (exterior angle of a triangle)
$\angle HGC = (100-60)^{\circ} = 40^{\circ}$ (exterior angle of a triangle)

This problem is taken from the UKMT Mathematical Challenges.