Angles in polygons

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?

Each interior angle of a particular polygon is an obtuse angle which is a whole number of degrees. What is the greatest number of sides the polygon could have?

This LOGO Challenge emphasises the idea of breaking down a problem into smaller manageable parts. Working on squares and angles.

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?