Angles in polygons

problem
Walking round a triangle

Age

5 to 7

Challenge level

This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?
problem
Which solids can we make?

Age

11 to 14

Challenge level

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
problem
Wood pile perimeter

Age

14 to 16

Challenge level

Weekly Problem 30 - 2011
Three touching circles have an interesting area between them...
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
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
Outside the nonagon

Age

11 to 14

Challenge level

Weekly Problem 44 - 2010
Extend two of the sides of a nonagon to form an angle. How large is this acute angle?
problem
Angle hunt

Age

11 to 14

Challenge level

Weekly Problem 39 - 2010
If you know three lengths and an angle in this diagram, can you find another angle by calculation?
problem
Cyclic quadrilaterals

Age

11 to 16

Challenge level

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
problem
Making sixty

Age

14 to 16

Challenge level

Why does this fold create an angle of sixty degrees?
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?