Angles in polygons

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
Angle to chord

Age

14 to 16

Challenge level

Weekly Problem 23 - 2008
A triangle has been drawn inside this circle. Can you find the length of the chord it forms?
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
Circled corners

Age

14 to 16

Challenge level

Three circles have been drawn at the vertices of this triangle. What is the area of the inner shaded area?
problem
Incentre angle

Age

14 to 16

Challenge level

Weekly Problem 1 - 2011
Use facts about the angle bisectors of this triangle to work out another internal angle.
problem
Wood pile perimeter

Age

14 to 16

Challenge level

Weekly Problem 30 - 2011
Three touching circles have an interesting area between them...
problem
Square triangle

Age

11 to 14

Challenge level

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

Age

14 to 16

Challenge level

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?