Angles in polygons

Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?

Can you match the Venn diagram with the Carroll diagram that shows the same information?

In this game, you turn over two cards and try to draw a triangle which has both properties.

What do you notice when you put three triangles together?

How many triangles have all three angles perfect squares (in degrees)?

Triangle ABC has a right angle at C. ACRS and CBPQ are squares. ST and PU are perpendicular to AB produced. Show that ST + PU = AB

Weekly Problem 53 - 2012
ABCDEFGHI is a regular nine-sided polygon (called a 'nonagon' or 'enneagon'). What is the size of the angle FAE ?

Creating designs with squares - using the REPEAT command in LOGO. This requires some careful thought on angles

Weekly Problem 30 - 2011
Three touching circles have an interesting area between them...

A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?