Angles in polygons

problem
Pentakite

Age

14 to 18

Challenge level

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

Age

14 to 16

Challenge level

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

Age

11 to 14

Challenge level

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.
problem
Dodecawhat

Age

14 to 16

Challenge level

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.
problem
Transformations on a pegboard

Age

7 to 11

Challenge level

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

Age

7 to 11

Challenge level

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

Age

11 to 14

Challenge level

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

Age

14 to 18

Challenge level

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.
problem
Tricircle

Age

14 to 16

Challenge level

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.
problem
Floored

Age

14 to 16

Challenge level

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?