Angles - points, lines and parallel lines

Weekly Problem 35 - 2009
Two equilateral triangles have been drawn on two adjacent sides of a square. What is the angle between the triangles?

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

Weekly Problem 44 - 2010
Extend two of the sides of a nonagon to form an angle. How large is this acute angle?

My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the minute hand and hour hand had swopped places. What time did the train leave London and how long did the journey take?

An equilateral triangle is constructed on BC. A line QD is drawn, where Q is the midpoint of AC. Prove that AB // QD.

What is the sum of the angles of a triangle whose sides are circular arcs on a flat surface? What if the triangle is on the surface of a sphere?

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

Weekly Problem 45 - 2007
What is the obtuse angle between the hands of a clock at 6 minutes past 8 o'clock?

Weekly Problem 53 - 2007
The diagram shows a regular pentagon and regular hexagon which overlap. What is the value of x?