Angles in polygons

The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and two sides of the triangle. If the small circle has radius 1 unit find the radius of the larger circle.

Weekly Problem 50 - 2012
The diagram shows a regular dodecagon. What is the size of the marked angle?

Weekly Problem 18 - 2007
A regular pentagon together with three sides of a regular hexagon form a cradle. What is the size of one of the angles?

The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

Weekly Problem 27 - 2007
Ten stones form an arch. What is the size of the smallest angles of the trapezoidal stones?

How can you make an angle of 60 degrees by folding a sheet of paper twice?

The graph below is an oblique coordinate system based on 60 degree angles. It was drawn on isometric paper. What kinds of triangles do these points form?

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

Drawing the right diagram can help you to prove a result about the angles in a line of squares.