G C S E

[kuiperbelt]

Please see link below:

https://ibb.co/zVTKFG3

[JJ109]

The internal angle of a decagon = 144 degrees
Therefore X = 360 = 2(144)
= 360 -288 = 72 degrees

[Prudie]

Yep and if you want to know the total angles of any regular polygon with sides n then it's (2n - 4) x 90 degrees
So for a 10 sided it's 16 x 90 = 14440
Divide by n (or 10 in this case) to get the size of each interior angle so 1440/10 = 144
Each exterior angle is 180 - 144 = 36
So in this case 2 together makes 72.

[Prudie]

16 x 90 = 1440
I have long nails and sometimes press the keys too hard and get a double entry :-)

[ToraToraTora]

...or (n-2)*180

[ToraToraTora]

^^^ instead of (2n - 4) x 90

[bobbinwales]

oh i remember doing these before ... I use to forget the formula for internal angles so I finded it easier to remember exterior angles add up to 360.
So in a decagon each of 10 exterior angles is 36 degrees.
So each interior is 180-36=144 as there angles on a straight line and make 180.
Then the angle X is 360-144-144=72
Same answer as other's above.... just showing an other slightly diffrent way

[Prudie]

And in this case yours is probably the easier to remember and get the solution bobb.

[ZebuSanctuary]

Agree with all the answers provided above.

However, I am claiming BA on the strength that Prudie has over complicated the formula for the sum of interior angles of a polygon.

Furthermore, the limits on 'n' have not been specified.

Let me proffer;

Polygon Sum = (n - 2) x 180 where n ≥ 3

;-)

[Prudie]

I certainly have not overcomplicated it, when said in words it's easy and how I remember it from school
two n minus 4 right angles
:-)

[Prudie]

where n ≥ 3
That's probably because anything less than 3 sides (the triangle) is not a polygon so has no purpose even being mentioned.

[ToraToraTora]

kuiper: "Let me proffer;

Polygon Sum = (n - 2) x 180 where n ≥ 3 "

...as I did at 14:57, I therefore claim BA

[Peter Pedant]

yeah bo-bo
I did this 1961
2n-4 rt angles - as a formula to memorise
and then we did something else - - oh, z angles and F angles and adjacent angles ( sum = 180)
as a sort of soup of unconnected things

[Atheist]

I agree with bobbin...
If you start by looking at the horizontal line at the bottom of the decagon, then step it round the decagon side by side till it gets back to its starting point, it has turned itself through 360 degrees. It's done this in 10 steps, so each step is 36 degrees (i.e. external angles). So internal angles are 180-36=144.

[ZebuSanctuary]

// I certainly have not overcomplicated it //

This will be subject to mathematical rigour and subsequently reduced to a delineated form ;-)

The claim; (2n - 4) x 90 is not complicated.

The common factor within the parentheses is clearly the number 2

Simplifying the above and rewriting as

2(n - 2) x 90

which becomes

(n - 2) x 180 by the process of simplification.

There you have the incontrovertible truth.

Come on Kuiper,
wing that BA
over here. You
know it makes
sense ;-)

[ToraToraTora]

"Simplifying the above and rewriting as

2(n - 2) x 90

which becomes

(n - 2) x 180 by the process of simplification. "

- which I said at 14:57, BA is mine surely!

[Prudie]

You guys have all utterly missed my point. We learnt it as a phrase not a written down equation. A phrase that is easier to recall in words than algebraic terms - I repeat two n minus 4 right angles
You can stick your BA wherever you lie
:-)

[kuiperbelt]

Acknowledging JJ109 speedy answer but grandson thinks most comprehensive answer has been provided by Prudie. So BA to you!!

ToraToraTora and Zebu you were both clutching at straws but you knew that didnt you LOL

If it's any consolation, grandson actually thinks (n-2) x 180 is easier to remember!!

[kuiperbelt]

>14.41 Inspite of arithmetical error you were quick to rectify it straight after LOL :-)