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There are **50** NRICH Mathematical resources connected to **Angles in polygons**, you may find related items under Angles, polygons, and geometrical proof.

Problem
Primary curriculum
Secondary curriculum
### Name That Triangle!

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangle or No Triangle?

Here is a selection of different shapes. Can you work out which ones are triangles, and why?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Angles Inside

Draw some angles inside a rectangle. What do you notice? Can you prove it?

Age 11 to 14

Challenge Level

Problem
Live Primary curriculum
Secondary curriculum
### Always, Sometimes or Never? Shape

Are these statements always true, sometimes true or never true?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Polygon Pictures

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Star Polygons

Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Isosceles Seven

Is it possible to find the angles in this rather special isosceles triangle?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Polygon Rings

Join pentagons together edge to edge. Will they form a ring?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Round a Hexagon

This problem shows that the external angles of an irregular hexagon add to a circle.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Walking Round a Triangle

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?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Which Solids Can We Make?

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cyclic Quadrilaterals

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

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Semi-regular Tessellations

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangles All Around

Can you find all the different triangles on these peg boards, and find their angles?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangles in Circles

Can you find triangles on a 9-point circle? Can you work out their angles?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangles and Petals

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Terminology

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Transformations on a Pegboard

How would you move the bands on the pegboard to alter these shapes?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Quadrilaterals

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Data Duos

Can you match the Venn diagram with the Carroll diagram that shows the same information?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Possible Pairs

In this game, you turn over two cards and try to draw a triangle which has both properties.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Gibraltar Geometry

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Angles in Three Squares

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### LOGO Challenge 4 - Squares to Procedures

This LOGO Challenge emphasises the idea of breaking down a problem into smaller manageable parts. Working on squares and angles.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Logo Challenge 3 - Star Square

Creating designs with squares - using the REPEAT command in LOGO. This requires some careful thought on angles

Age 7 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### First Forward Into Logo 9: Stars

Turn through bigger angles and draw stars with Logo.

Age 11 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### First Forward Into Logo 7: Angles of Polygons

More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.

Age 11 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pegboard Quads

Make different quadrilaterals on a nine-point pegboard, and work out their angles. What do you notice?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangle Pin-down

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Diagonally Square

Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cartesian Isometric

The graph below is an oblique coordinate system based on 60 degree angles. It was drawn on isometric paper. What kinds of triangles do these points form?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fred the Class Robot

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Timber!

How can the school caretaker be sure that the tree would miss the school buildings if it fell?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Convex Polygons

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pentakite

Given a regular pentagon, can you find the distance between two non-adjacent vertices?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bow Tie

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Dodecawhat

Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.

Age 14 to 16

Challenge Level

Article
Primary curriculum
Secondary curriculum
### 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.

Age 11 to 16

Problem
Primary curriculum
Secondary curriculum
### Getting an Angle

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pent

The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tricircle

The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and two sides of the triangle. If the small circle has radius 1 unit find the radius of the larger circle.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Floored

A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Sameness Surely

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### No Right Angle Here

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Golden Triangle

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### At a Glance

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

Age 14 to 16

Challenge Level