Angles in polygons

problem

Nonagon Angle

Age

11 to 14

Challenge level

2 out of 3

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

2 out of 3

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

2 out of 3

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

2 out of 3

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

2 out of 3

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

2 out of 3

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

2 out of 3

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

2 out of 3

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

Getting an Angle

Age

11 to 14

Challenge level

3 out of 3

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

Convex Polygons

Age

11 to 14

Challenge level

3 out of 3

Show that among the interior angles of a convex polygon there cannot be more than three acute angles.