Angles - points, lines and parallel lines

Construct this design using only compasses

Weekly Problem 16 - 2007
Can you figure out how far the robot has travelled by the time it is first facing due East?

Weekly Problem 21 - 2009
What is the angle between the two hands of a clock at 2.30?

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?

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.