Angles in polygons

Weekly Problem 38 - 2008
A quadrilateral can have four right angles. What is the largest number of right angles an octagon can have?

Weekly Problem 50 - 2008
The lengths SP, SQ and SR are equal and the angle SRQ is x degrees. What is the size of angle PQR?

Given a regular pentagon, can you find the distance between two non-adjacent vertices?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Show that among the interior angles of a convex polygon there cannot be more than three acute angles.

Make different quadrilaterals on a nine-point pegboard, and work out their angles. What do you notice?

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Which hexagons tessellate?

Weekly Problem 39 - 2010
If you know three lengths and an angle in this diagram, can you find another angle by calculation?

Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.