Angles in polygons

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

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.

How would you move the bands on the pegboard to alter these shapes?

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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

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.

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.

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?