Angles in polygons

problem
A sameness surely

Age

14 to 16

Challenge level

Triangle ABC has a right angle at C. ACRS and CBPQ are squares. ST and PU are perpendicular to AB produced. Show that ST + PU = AB
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
Darts and kites

Age

14 to 16

Challenge level

Explore the geometry of these dart and kite shapes!
problem
Golden triangle

Age

16 to 18

Challenge level

Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.
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?
article
Arclets explained

This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.
problem
Always, sometimes or never? Shape

Age

7 to 11

Challenge level

Are these statements always true, sometimes true or never true?
problem
Gibraltar geometry

Age

11 to 14

Challenge level

Take a look at the photos of tiles at a school in Gibraltar. What questions can you ask about them?
problem
Angles in three squares

Age

14 to 16

Challenge level

Drawing the right diagram can help you to prove a result about the angles in a line of squares.
problem
Polygon pictures

Age

11 to 14

Challenge level

Can you work out how these polygon pictures were drawn, and use that to figure out their angles?