Polygon Riddle 2


My first is in shape but not in space;

My second is in line and also in place;

My third is in point but not in line;

My fourth in operation but not in sign;

My fifth is in angle but not in degree;

My sixth is in glide but not symmetry;

My seventh in round but not in square;

My last is in patterns you see everywhere;

My whole is a polygon, regular not wide;

But what is the sum of the angles inside?

Hint: split the shape into triangles

A Mathematics Lesson Starter Of The Day


Topics: Starter | Riddles | Shape

  • Transum,
  • This form of a riddle or word puzzle used to be more popular than it is today. The structure of the riddle is that each line (the first seven lines in this case) gives a clue to a single letter of the answer. The last line (the eighth line in this case) then gives a clue to the complete answer.
    You can work out from line one that the first letter of the answer occurs in the word ‘shape’ but it does not occur in the word ‘space'. By process of elimination you can see that the first letter of the answer must be H.
    Work through the other lines of the riddle to determine the other letter possibilities and then you are well on your way to solving the riddle.
  • Hayley Roberts, Gloucestershire
  • The last line of the riddle asks what is the total of the inside angles of the polygon and the answer states 900 degrees. I do not believe this to be correct as the total of the internal angles of any polygon only add up to 360 degrees.
  • Tracey Roden, ICC
  • I thought it was the EXTERNAL angles of a polygon which total 360! Think triangle - the internal angles add up to 180!!
  • Doyle,
  • The exterior angles sum to 360
    and the interior angles depends on how many sides the shape has,
    a heptagon has 7 sides and therefore it can be split into 5 triangles
    a triangle has 180 degrees, so 180*5 = 900.
  • Rob Irving, Higham
  • Internal angles of any polygon follow the formula n-2 x 180 where n= the number of sides of the polygon so the reason that a triangle has 180 degrees is becan(which = 3) - 2 x 180 means 1 x 180.
    Try the formula for a rectangle and you get 360 degrees.
    And yes it's true for all polygons. External angles are different they add up to 360.

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.

If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:

Excellent, I would like to see more like this
Good, achieved the results I required
Didn't really capture the interest of the students
Not for me! I wouldn't use this type of activity.

This starter has scored a mean of 3.0 out of 5 based on 243 votes.

Previous Day | This starter is for 28 July | Next Day



Sign in to your Transum subscription account to see the answers

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items chosen and recommended by Transum Mathematics to get you started.


Have you read Craig's book yet?

Craig Barton must surely be the voice of Mathematics teachers in the UK. His wonderful podcasts interviewing the industry experts have culminated in this wonderful book. As Craig says: "I genuinely believe I have never taught mathematics better, and my students have never learned more. I just wish I had known all of this twelve years ago..." more...

"How I wish I'd taught Maths" is an extraordinary and important book. Part guide to research, part memoir, part survival handbook, it’s a wonderfully accessible guide to the latest research on teaching mathematics, presented in a disarmingly honest and readable way. I know of no other book that presents as much usable research evidence on the dos and don’ts of mathematics teaching in such a clear and practical way. No matter how long you have been doing it, if you teach mathematics—from primary school to university—this book is for you." Dylan Wiliam, Emeritus Professor of Educational Assessment, UCL.

The Craig Barton Book

Casio Classwiz Calculator

There is currently a lot of talk about this new calculator being the best in its price range for use in the Maths classroom. The new ClassWiz features a high-resolution display making it easier to view numerical formulas and symbols but it isn't a graphical calculator as such (it has the capacity to draw graphs on your smart phone or tablet, via a scannable QR code and an app).

As well as basic spreadsheet mode and an equation solving feature you also get the ability to solve quadratic, cubic or quartic polynomial inequalities and the answer is given just as it should be written down, using the correct inequality symbols!

This calculator has a high-performance processor and twice the memory of previous models ensuring speedy operation and superior computational power.more...

Online Maths Shop

Laptops In Lessons

Teacher, do your students have access to computers?
Do they have iPads or Laptops in Lessons?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Laptops In Lessons

Here a concise URL for a version of this page without the comments.



Here is the URL which will take them to a related student activity.


Maths Riddles


Here is the URL which will take them the Transum Riddle collection. Enjoy!


Student Activity


Curriculum Reference

See the National Curriculum page for links to related online activities and resources.


©1997-2020 WWW.TRANSUM.ORG