# Polygon Riddle 2

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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

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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.

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