Angles in polygons

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?
problem

No Right Angle Here

Age

14 to 16

Challenge level

Prove that the internal angle bisectors of a triangle will never be perpendicular to each other.
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

Convex Polygons

Age

11 to 14

Challenge level

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

Heptagon Has

Age

11 to 14

Challenge level

Weekly Problem 15 - 2012
How many of the five properties can a heptagon have?
problem

Parallelogram in the Middle

Age

11 to 14

Challenge level

Weekly Problem 27 - 2013
The diagram shows a parallelogram inside a triangle. What is the value of $x$?