Angles in polygons

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

Nonagon Angle

Age

11 to 14

Challenge level

Weekly Problem 53 - 2012
ABCDEFGHI is a regular nine-sided polygon (called a 'nonagon' or 'enneagon'). What is the size of the angle FAE ?
problem

Integral Polygons

Age

11 to 14

Challenge level

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?
problem

Dodecagon Angles

Age

11 to 14

Challenge level

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

Hexapentagon

Age

11 to 14

Challenge level

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

U in a Pentagon

Age

11 to 14

Challenge level

Weekly Problem 18 - 2008
The diagram shows a regular pentagon. Can you work out the size of the marked angle?
problem

Right Angled Octagon

Age

11 to 14

Challenge level

Weekly Problem 38 - 2008
A quadrilateral can have four right angles. What is the largest number of right angles an octagon can have?
problem

Triangle Split

Age

11 to 14

Challenge level

Weekly Problem 50 - 2008
The lengths SP, SQ and SR are equal and the angle SRQ is x degrees. What is the size of angle PQR?
problem

Square Triangle

Age

11 to 14

Challenge level

How many triangles have all three angles perfect squares (in degrees)?
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?