The document presents a triangle puzzle where the angles of the triangle are required to be square numbers. It provides clues such as the total of three angles in a triangle being 180 degrees and defines square numbers as numbers multiplied by themselves. The answer is then revealed to be that the three angles are 100, 64, and 16 degrees, corresponding to the square numbers 10x10, 8x8, and 4x4, which sum to 180 degrees.

1. © MathSphere www.mathsphere.co.uk
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A square triangle ?????????
This is a problem for our older puzzlers.
It may seem very peculiar to you but I've just drawn
a triangle where all the angles are square.
No, I don't mean right angles or 900
- that's
impossible!
What I do mean is that each angle, measured in
degrees, is a square number.
Can you tell me how many degrees each of the
angles is?
Help!
Clue: the total of the three angles
in a triangle is 1800
.
Can you remember what
square numbers are?
Try 1 x 1, 2 x 2, etc
Find the answer on the next page.

2. © MathSphere www.mathsphere.co.uk
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A square triangle - answer
Remember the problem: a triangle with all the
angles being square numbers!
The clue was that the total of the three angles
in a triangle is 1800
.
You get a square number by multiplying a number by
itself, so:
The square numbers are:
1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 = 49
8 x 8 = 64
9 x 9 = 81
10 x 10 = 100
There are three angles in
a triangle (Yes there
are!) so which three
square numbers make
180 ?
The answer is:
100 + 64 + 16